Physics 123

23. Light: Geometric Optics

23.1 The Ray Model of Light

23.2 Reflection - Plane Mirror

23.3 Spherical Mirrors

23.5 Refraction - Snell’s law

23.7 Converging and Diverging Lenses

Reflection

i

r

i = r

Angle of incidence equals the angle of reflection

Image in a Plane Mirror

Image in a Plane Mirror

Image in a Plane Mirror

Image in a Plane Mirror

Image in a Plane Mirror

Image in a Plane Mirror

do = di

Spherical Mirrors

Concave mirror Convex mirror

Concave Mirror

radius = rfocus = f

r f

f = r /2

Concave Mirror

A parallel ray reflects through the focus

Concave Mirror

Solar Cooker!

Concave Mirror

A ray through the focus reflects parallel

Concave Mirror

Image is inverted, real, reduced

Concave Mirror Equation

1 / d o + 1 / d i = 1 / f

Concave Mirror Problem

A 3 cm high candle is located 5 cm from a concave mirror whose radius of curvature is 20 cm. What are the characteristics of the image?

Concave Mirror Problem

f = 10 cm

1/do + 1/ di = 1/f

1/5 + 1/ di = 1/10

1/ di = - 1/10

di = - 10 cm

The image is 10 cm behind the mirror, virtual, upright, and magnified 2X

m = - di / do

Concave Mirror Problem

Makeup mirror!

If the object is within the focus of the concave mirror the image is enlarged (magnified), upright

but virtual … it’s all in your head!!!

Convex Mirror

Convex Mirror

Image will ALWAYS be reduced, virtual, upright

Jurassic Park!

Rear View Mirror

Objects in the mirror are closer than they appear!

Convex Mirror Equation

1 / d o + 1 / d i = 1 / f

Note: f is negative

d i is negative

Convex Mirror Problem

A 3 cm high candle is located 5 cm from a convex mirror whose radius of curvature is 20 cm. What

are the characteristics of the image?

Convex Mirror Problem

f = - 10 cm

1/do + 1/ di = 1/f

1/5 + 1/ di = - 1/10

1/ di = - 3/10

di = - 3.3 cm

The image is 3.3 cm behind the mirror, virtual, upright, and reduced in size

m = - di / do

m = 1 / 3

Refraction

i

r

Index of Refraction

n = sin i / sin r

Refraction Problem

The index of refraction of glass is 1.5. A ray of light is incident on a glass pane at an angle of 600. Calculate the angle of refraction.

Refraction Problem

n = sin i / sin r

1.5 = sin 600 / sin r

1.5 = 0.866 / sin r

sin r = 0.866 / 1.5

sin r = 0.58

r = 350

Converging (convex) Lens

Converging Lens

When the object is outside the focus, the image is real and inverted

Converging Lens

When the object is inside the focus, the image is virtual, upright, and enlarged.

Diverging (concave) Lens

Diverging (concave) Lens

Diverging (concave) Lens

The image is ALWAYS reduced, upright, virtual

Lens Problem

A 35 mm slide projector uses a converging lens with f = 20 cm. The screen is 3 m away. How far is the slide from the lens?

Lens Problem

1/do + 1/ di = 1/f

1/do + 1/ 300 = 1/20

1/do = 1/20 - 1/ 300

do = 21. 4 cm

m = - di / do

m = - 300 / 21.4

m = -14

Image is real, inverted, magnified

That’s all folks!