Optics

The Study of Light

Areas of Optics

Geometric OpticsLight as a ray.

Physical OpticsLight as a wave.

Quantum OpticsLight as a particle.

Optical images• Nature

• real (converging rays)• virtual (diverging rays)

• Orientation• upright• inverted

• Size• true• enlarged• reduced

Law of Reflection• Angle of incidence equals angle of reflection.

i

r

Plane Mirror

+ -

object5 cm

Image-5 cm

Spherical mirrors

shiny shiny

concave convex

+ + --(where reflected rays go) (where reflected rays go) (dark side)(dark side)

Focal length, f, is positive Focal length, f, is negative

Parts of aSpherical Concave Mirror

Principle axis

VertexCenter

Focus

+ -

Spherical Concave Mirror(object outside center)

C F

Real, Inverted, Reduced Image

p

f

c

C F

Real, Inverted, True Image

Spherical Concave Mirror(object at center)

C F

Real, Inverted, EnlargedImage

Spherical Concave Mirror(object between center and focus)

C F

No image

Spherical Concave Mirror(object at focus)

C F

Virtual, Upright, Enlarged Image

Spherical Concave Mirror(object inside focus)

Parts of aSpherical Convex Mirror

Principle axis

CenterFocus

+ -

Spherical Convex Mirror

F C

Virtual, Upright, Reduced Image

Mirror equation #1•1/si + 1/so = 1/f

•si: image distance

•so: object distance•f: focal length

Mirror equation # 2• M = -si/so = hi/ho

• si: image distance• so: object distance• hi: image height• ho: object height• M: magnification

Concave vs convex mirrors Concave

Image is real when object is outside focus

Image is virtual when object is inside focus

Focal length f is positive

Convex Image is always

virtual

Focal length f is negative

Real vs Virtual images Real

Formed by converging light rays

si is positive when calculated with mirror equation

Virtual Formed by

diverging light rays

si is negative when calculated with mirror equation

Upright vs Inverted images Upright

Always virtual if formed by one mirror or lens

hi is positive when calculated with mirror/lens equation

Inverted Always real if

formed by one mirror or lens

hi is negative when calculated with mirror/lens equation

Definition: Refraction

Change in speed of light as it moves from one medium to another.

Can cause bending of the light at the interface between media.

Index of Refraction speed of light in vacuum

speed of light in medium

n = c/v

n =

Snell’s Law

n1

n2

1

angle of incidence

2

angle of refraction

n1sin 1 = n2sin 2

n1 < n2

n1

n2

1

2

light bends toward normal

n1 > n2

n1n2

1

2

light bends away from normal

Dispersion

The separation of white light into colors due to different refractive indices for different wavelengths.

DispersionDue to different indices of refraction for different wavelengths of light.

Critical Angle of Incidence

n1

n2

c

Light would refract 90o so it reflects instead, undergoing total internal reflection.

r

n1 > n2

Calculating Critical Angle

n1sin(1) = n2sin(2)

n1sin(90o) = n2sin(2)

n1 = n2sin(c)

Total Internal Reflection

n1

n2

i r

Occurs only when angle of incidence > critical angle

Announcements 04/18/23

Turn in homework (lens problems) on overhead.

Lab report will be due next week (on looseleaf or graph paper).

Consider a lens with f = 20 cm.

You place a 5 cm tall object 30 cm in front of the lens.

a)Draw the ray diagram and construct the image.

b)Calculate the image distance and height using the lens/mirror equations.

c)Name the image.

Converging lens #1

C F

Real, Inverted, Reduced Image

F2F 2F

+-

Converging lens #2

C F

Real, Inverted, True Image

F2F 2F

+-

Converging lens #3

C F

Real, Inverted, Enlarged Image

F2F

+-

Converging lens #4

C F

Virtual, Upright, Enlarged Image

F

+-

For converging lenses

• f is positive• so is positive• si is positive for real images and

negative for virtual images• M is negative for real images

and positive for virtual images • hi is negative for real images

and positive for virtual images

Diverging lens

C F

Virtual, Upright, Reduced Image

F

+-

For diverging lenses

• f is negative• so is positive• si is negative• M is positive and < 1• hi is positive and < ho