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Page 1: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Drawing Ray Diagrams

Concave and Convex Mirrors and Double Concave and Double

Convex Lenses

By Vincent Sapone

Page 2: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

1. First ray goes parallel to the mirror and then reflects back down through the focus.

2. Second Ray goes through the focus and into the mirror and then reflected back parallel to

axis.3. Ray drawn to center of lens and reflects back

downwards at an equal angle (symmetric)4. If at or within the focal length you an draw a

line perpendicular to the mirror so that it goes back through itself and into the center of

curvature (R = 2f). This can replace the second ray above which now cannot be drawn.

Page 3: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• Rule 1 First ray goes parallel to the mirror and then reflects back down through the focus.

Page 4: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

Ray 1

Ray 2

• Second Ray goes through the focus and into the mirror and then reflected

back parallel to axis.

Page 5: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• Ray drawn to center of lens and reflects back

downwards at an equal angle (symmetric) Ray 1

Ray 2

Ray 3

Page 6: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

Lets draw ray diagrams for the following cases:

• do = f

• f<do<R

• do>R

• do>f

• do=R

Page 7: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

• Object is on the Focal Point

• Do = F

Page 8: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

Page 9: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do = f

Page 10: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do = f

Page 11: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do = f

Page 12: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do = f

Ray 1

Page 13: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do = f

Ray 1Cannot Draw 2nd ray from Object through focus.

Page 14: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do = f

Ray 1Cannot Draw 2nd ray from Object through focus.

Ray 3

Page 15: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do = f

Ray 1Cannot Draw 2nd ray from Object through focus.

Ray 3

They do not Cross:

No Image!

Page 16: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do = f

Ray 1Cannot Draw 2nd ray from Object through focus.

Ray 3

They do not Cross:

No Image!

Even a fourth ray will not cross the others.

Ray 4

Page 17: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

• Object is Between Focal Point and Center of Curvature

• f<do<R

Page 18: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• f<do<R

Page 19: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• f<do<R

Ray 1

Page 20: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• f<do<R

Ray 1

Ray 2

Page 21: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• f<do<R

Ray 1

Ray 2

Ray 3

Page 22: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• f<do<R

Ray 1

Ray 2

Ray 3 Real Image:

Magnified

Page 23: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

• Object distance is Greater than or outside the radius of curvature (C)

• do>R

Page 24: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do>R

Page 25: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do>R

Ray 1

Page 26: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do>R

Ray 1

Ray 2

Page 27: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do>R

Ray 1

Ray 2

Ray 3

Page 28: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do>R

Ray 1

Ray 2

Ray 3Image Real and Demagnified

Page 29: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

• Object distance is smaller than or within the radius of curvature (C)

• do<f

Page 30: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do<f

Page 31: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do<f

Ray 1

Page 32: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do<f

Ray 1

Ray 2

Page 33: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do<f

Ray 1

Ray 2

Ray 3

Page 34: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Is there an Image?

What do you think?

Page 35: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do<f

Ray 1

Ray 2

Ray 3

Page 36: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do<f

Ray 1

Ray 2

Ray 3

Page 37: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do<f

Ray 1

Ray 2

Ray 3

Page 38: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do<f

Ray 1

Ray 2

Ray 3Image is Virtual, Right side up and Magnified

Page 39: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Compare this to the First Example with no Image.

Why Didn’t that one have a virtual image?

Page 40: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do = f

Ray 1

Ray 2

Cannot Draw 3rd ray from Object through focus.

Ray 4

Page 41: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

The Rays appear to be pretty much parallel.

Therefore they will not cross on either side so

there is no image, virtual or real.

Page 42: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

• Object distance is equal to radius of curvature

• do = R

Page 43: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do = R

Page 44: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do = R

Page 45: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do = R

Ray 1

Page 46: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do = R

Ray 1

Page 47: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do = R

Ray 1

Ray 2

Page 48: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do = R

Ray 1

Ray 2

Page 49: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do = R

Ray 1

Ray 2

Ray 3

Page 50: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do = R

Ray 1

Ray 2

Ray 3

Page 51: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror

FC

• do = R

Ray 1

Ray 2

Ray 3

Image is Real, upside down and demagnified.

Page 52: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Cosmetics

• This is a cosmetics mirror.

• Up close (do <f) you are right side up and appear magnified.

• As you move away your image will eventually invert and become smaller.

Page 53: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

1. First ray goes parallel to the mirror and then reflects back up (dotted image line goes

through focus on the other side).2. Second Ray is aimed directly at the center of

curvature on the other side but once it hits the mirror it reflects back through itself with the

dotted image line going through C).3. Ray drawn aimed at focus on the other side

and reflect off the mirror parallel to the axis (dotted line drawn parallel in the other

direction)

Page 54: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

• We shall now draw Convex Mirror Diagrams for the following cases:

• do>R• f<do>R

• do<f

Page 55: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

• Distance to Object is greater than radius of curvature

• do > R

Page 56: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

Page 57: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do>R

Page 58: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do>R

Page 59: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do>R

Page 60: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do>R

Ray 1

Page 61: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do>R

Ray 1

Page 62: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do>R

Ray 1

Page 63: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do>R

Ray 1

Page 64: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do>R

Ray 1

Ray 2

Page 65: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do>R

Ray 1

Ray 2

Page 66: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do>R

Ray 1

Ray 2

Page 67: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do>R

Ray 1

Ray 2

Ray 3

Page 68: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do>R

Ray 1

Ray 2

Ray 3

Page 69: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do>R

Ray 1

Ray 2

Ray 3

Image Virtual, Right Side up Demagnified

Page 70: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

• Distance to Object is in between focus and radius of curvature.

f<do<R

Page 71: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

F<do<R

Page 72: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

F<do<R

Page 73: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

F<do<R

Page 74: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

F<do<R

Page 75: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

F<do<R

Ray 1

Page 76: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

F<do<R

Ray 1

Page 77: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

F<do<R

Ray 1

Page 78: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

F<do<R

Ray 1Ray 2

Page 79: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

F<do<R

Ray 1Ray 2

Page 80: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

F<do<R

Ray 1Ray 2

Page 81: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

F<do<R

Ray 1Ray 2

Page 82: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

F<do<R

Ray 1Ray 2

Ray 3

Page 83: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

F<do<R

Ray 1Ray 2

Ray 3

Page 84: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

F<do<R

Ray 1Ray 2

Ray 3

Page 85: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

f<do<R

Ray 1Ray 2

Ray 3

Image: Virtual, right side up, demagnified.

Page 86: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

• Distance to Object less than the distance to the focus

do<f

Page 87: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do<f

Page 88: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do<f

Page 89: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do<f

Page 90: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do<f

Page 91: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do<f

Page 92: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do<f

Ray 1

Page 93: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do<f

Ray 1

Page 94: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do<f

Ray 1

Page 95: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do<f

Ray 1

Page 96: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do<f

Ray 1

Ray 2

Page 97: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do<f

Ray 1

Ray 2

Page 98: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do<f

Ray 1

Ray 2

Page 99: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do<f

Ray 1

Ray 2

Ray 3

Page 100: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do<f

Ray 1

Ray 2

Ray 3

Page 101: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do<f

Ray 1

Ray 2

Ray 3

Page 102: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Mirror

F C

do<f

Ray 1

Ray 2

Ray 3

Image Virtual, right side up, demagnified

Page 103: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

• For the Following Conditions

do=f f<do<2f do>2f do<f do=2f

• Note the lens thickness is to be assumed small so that refraction is not a concern.

Page 104: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex Lens Rules

• First ray is drawn parallel to principal axis until it strikes the center of the mirror. It then converged down on through the focal point on the other side of the lens.

• The second ray has a straight line drawn from the object to the focus to the lens on the same side and then it refracts parallel to the principal axis on the other side.

• The third ray is usually drawn in a direction from the object through the center of the lens itself into the other side.

Page 105: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

Ray 1

First ray is drawn parallel to principal axis until it strikes the center of the mirror. It then converged down on

through the focal point on the other side of the lens

Page 106: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

Ray 1

Ray 2

The second ray has a straight line drawn from the object to the focus to the lens on the same side and then it refracts parallel to the principal axis on the other side.

Page 107: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

Ray 1

Ray 2

Ray 3The third ray is usually drawn in a direction from the object through the center of the lens itself into the other side.

Page 108: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

• Distance to Object is in between focus and radius of curvature.

do=f

Page 109: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do=f

Page 110: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do=f

Page 111: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do=f

Page 112: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do=f

Ray 1

Page 113: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do=f

Ray 1

Ray 2

Page 114: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do=f

Ray 1

Ray 2

Cannot Draw Ray Three Through Focus as the object is on the focus.

Page 115: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do=f

Ray 1

Ray 2

Cannot Draw Ray Three Through Focus as the object is on the focus.

No Image!

Page 116: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

f<do<2f

Page 117: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

f<do<2f

Page 118: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

f<do<2f

Ray 1

Page 119: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

f<do<2f

Ray 1

Ray 2

Page 120: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

f<do<2f

Ray 1

Ray 2

Ray 3

Page 121: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

f<do<2f

Ray 1

Ray 2

Ray 3

Page 122: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

f<do<2f

Ray 1

Ray 2

Ray 3

Real Image, Inverted and

Magnified

Page 123: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do>2f

Page 124: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do>2f

Ray 1

Ray 2

Page 125: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do>2f

Ray 1

Ray 2

Ray 3

Page 126: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do>2f

Ray 1

Ray 2

Ray 3

Image is Real Upside Down Demagnified

Page 127: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do<f

Page 128: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do<f

Ray 1

Page 129: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do<f

Ray 1

Ray 2

Page 130: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do<f

Ray 1

Ray 2

Cannot Draw Ray 3 but there is an

image still!

Page 131: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do<f

Ray 1

Ray 2

Cannot Draw Ray 3 but there is an

image still!

Page 132: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do<f

Ray 1

Ray 2

Cannot Draw Ray 3 but there is an

image still!

Page 133: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do<f

Ray 1

Ray 2

Image is Virtual Upside Down and really magnified

Page 134: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do=2f

Page 135: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do=2f

Ray 1

Page 136: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do=2f

Ray 1

Ray 2

Page 137: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do=2f

Ray 1

Ray 2

Ray 3

Page 138: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Convex or Converging Lens

FF

do=2f

Ray 1

Ray 2

Ray 3

Image Real Upside Down

Magnified

Page 139: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Magnifying Glass

• This double convex lens is how a magnifying glass works.

• When at the focus (do=f) there is no image (very blurry).• When close (do<f) it magnifies an image which appears

normal (right side up).• As you move farther the image will appear to be upside

down buy magnified.• As you move even farther the image will stay inverted

but get smaller.

• Try it out next time you have a magnifying glass!!!!

Page 140: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

• For the Following Conditions

do=f f<do<2f do>2f do<f

• Note the lens thickness is to be assumed small so that refraction is not a concern.

Page 141: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Rules for Concave Lenses

• 1st ray is drawn parallel to principle axis and hits the lens. It will refract upwards with its reversibility going through the focal point on the same side.

• 2nd ray is drawn from the object in a direction diagonal to the focal point on the other side but goes parallel to the principal axis once it crossed the lens.

• 3rd ray is drawn from the object straight through the center of the lens.

Page 142: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

Ray 1

Rule One : Parallel to axis once it hits lens. Goes diagonally upwards with

reversisibility going through focus on same side.

Page 143: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

Ray 1

Ray 2

Rule Two : Toward focus on other side but parallel to axis

once it hits lens.

Page 144: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

Ray 1

Ray 2

Ray 3Rule Three : Straight

through the center of the lens into the other side.

Page 145: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do=f

Page 146: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do=f

Ray 1

Page 147: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do=f

Ray 1

Ray 2

Page 148: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do=f

Ray 1

Ray 2

Ray 3

Page 149: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do=f

Ray 1

Ray 2

Ray 3

Page 150: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do=f

Ray 1

Ray 2

Ray 3

Page 151: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do=f

Ray 1

Ray 2

Ray 3

Image Virtual Right Side Up Demagnified

Page 152: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do>2f

Page 153: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do>2f

Ray 1

Page 154: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do>2f

Ray 1

Ray 2

Page 155: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do>2f

Ray 1

Ray 2

Ray 3

Page 156: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do>2f

Ray 1

Ray 2

Ray 3

Page 157: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do>2f

Ray 1

Ray 2

Ray 3

Page 158: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do>2f

Ray 1

Ray 2

Ray 3Image Virtual Right Side Up Demagnified

Page 159: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

f<do<2f

Page 160: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

f<do<2f

Ray 1

Page 161: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

f<do<2f

Ray 1

Ray 2

Page 162: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

f<do<2f

Ray 1

Ray 2

Ray 3

Page 163: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

f<do<2f

Ray 1

Ray 2

Ray 3

Page 164: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

f<do<2f

Ray 1

Ray 2

Ray 3

Page 165: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

f<do<2f

Ray 1

Ray 2

Ray 3Image Virtual Right Side Up Demagnified

Page 166: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do<f

Page 167: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do<f

Ray 1

Page 168: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do<f

Ray 1

Ray 2

Page 169: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do<f

Ray 1

Ray 2

Ray 3

Page 170: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do<f

Ray 1

Ray 2

Ray 3

Page 171: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do<f

Ray 1

Ray 2

Ray 3

Page 172: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave or Diverging Lens

FF

do<f

Ray 1

Ray 2

Ray 3

Image Virtual Right side Up Demagnified

Page 173: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Sign Conventions (Spherical Mirrors & Lenses)

Quantity Conditions Sign

Focal Length f Concave Mirror +Remember one remember all Convex Mirror -CCM is Positive Convex Lens +

Concave Lens -

Object Distance (do) Mostly Always +

Image Distance (di) Image Real +Does not depend on side it is on. Image Virtual -

Magnification (M) Image Upright +

Image Inverted -

Page 174: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Spherical Mirrors Spherical Lenses

Concave ConvexConvex

(Converging)Concave

(Diverging)

Condition Results Condition Results Condition Results Condition Results

do=f No Image do>R

Virtual

Right side up

Demagnified

do=f No image do=f

Virtual

Right Side Up

Demagnified

f<do<R

Real

Upside down.

Magnified.

f<do<R

Virtual

Right side up

Demagnified

f<do<2f

Real

Upside Down

Magnified

do>2f

Virtual

Right Side Up

Demagnified

do>R

Real

Demagnified

Upside Down

do<f

Virtual

Right side up

Demagnified

do>2f

Real

Upside Down

Demagnified

f<do<2f

Virtual

Right Side Up

Demagnified

do<f

Virtual

Magnified

Right Side up

do<f

Virtual

Right Side up

Magnified

do<f

Virtual

Right Side Up

Demagnfied

do=R

Real

Upside Down

Demagnified

do=2f

Real

Upside Down

Magnified

Page 175: Drawing Ray Diagrams Concave and Convex Mirrors and Double Concave and Double Convex Lenses By Vincent Sapone

Concave Mirror Convex Mirror

1. First ray goes parallel to the mirror and then reflects back down through the focus.

2. Second Ray goes through the focus and into the mirror and then reflected back parallel to axis.

3. Ray drawn to center of lens and reflects back downwards at an equal angle (symmetric)

4. If at or within the focal length you an draw a line perpendicular to the mirror so that it goes back

through itself and into the center of curvature (R = 2f). This can replace the second ray above

which now cannot be drawn.

1. First ray goes parallel to the mirror and then reflects back up (dotted image line goes

through focus on the other side).

2. Second Ray is aimed directly at the center of curvature on the other side but once it hits the

mirror it reflects back through itself with the dotted image line going through C).

3. Ray drawn aimed at focus on the other side and reflect off the mirror parallel to the axis

(dotted line drawn parallel in the other direction)

Concave Lens Convex Lens

1. 1st ray is drawn parallel to principle axis and hits the lens. It will refract upwards with its

reversibility going through the focal point on the same side.

2. 2nd ray is drawn from the object in a direction diagonal to the focal point on the other side but

goes parallel to the principal axis once it crossed the lens.

3. 3rd ray is drawn from the object straight through the center of the lens.

1. First ray is drawn parallel to principal axis until it strikes the center of the mirror. It then

converged down on through the focal point on the other side of the lens.

2. The second ray has a straight line drawn from the object to the focus to the lens on the same side and then it refracts parallel to the principal

axis on the other side.

3. The third ray is usually drawn in a direction from the object through the center of the lens

itself into the other side.


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