1

Last Time…

Reflection and refraction

Total internal reflection

Refraction •  Refraction occurs when light moves into

medium with different index of refraction. •  Result: light direction bends according to

Snell’s law

θi,1 θr

θ2

Angle of refraction

n1

n2 €

n1 sinθ1 = n2 sinθ2

Refraction angle

n2 < n1

v2>v1

Reflected ray

n1

n2 >n1

v2<v1

n1 Reflected ray

n2>n1 Refracted ray bent toward normal

n2<n1 Refracted ray bent away from normal

slower in medium 2 faster in medium 2

Why Snell’s law? •  Light moves at different speed in media with different

index of refraction.

θi θr

n1

n2>n1

θ2 v2<v1

Quick quiz Which of these fluids has the

smallest index of refraction (highest light speed)?

A

B

C

A.  Fluid A

B.  Fluid B

C.  Fluid C

D.  All equal

Numerical Example A beam of light is traveling underwater, aimed up at the

surface at 45˚ away from the surface normal. Part of it is reflected back into the water, and part is transmitted into the air.

Water n1=1.33

Air n2=1.00

θ1=45˚

€

n1 sinθ1 = n2 sinθ2

sinθ2 =n1n2sinθ1 = 0.94

θ2 = arcsin n1n2sinθ1

= 70˚

θ2

2

Quick quiz A trout looks up through

the surface at the setting sun, and at the moon directly overhead. He sees

A.  Moon directly overhead, sun ~ parallel to water surface

B.  Moon directly overhead, sun ~ 40˚ above water surface

C.  Moon ~ 40˚ from vertical, sun ~ parallel to water surface

D.  Moon and sun aligned at 40˚ from vertical.

n2=1.0

n1=1.33

Total Internal Reflection •  Is possible when light is directed from n1 > n2

⇒ refracted rays bend away from the normal

•  Critical angle: angle of incidence that will result in an angle of refraction of 90° (sinθ2 = 1)

For water:

€

sinθc =1

1.333= 0.75⇒θc = 48.75˚

Optical Fibers The cladding has a lower n than the core

•  Plastic or glass light pipes •  Applications:

–  Medicine: endoscope (light can be directed even if bent and the surgeon can view areas in the body using a camera.)

–  Telecommunications

Mon. Feb. 4, 2008 Physics 208, Lecture 4 10

Light rays and images

  Each point on object reflects light

  Light propagates out, represented by rays perpendicular to wavefront.

  Lens in our eye does some ‘imaging’ so that we identify origin of light rays.

Mon. Feb. 4, 2008 Physics 208, Lecture 4 11

Question

Does the fish appear

A.  Closer than actual

B.  Farther than actual

C.  Same as actual

n=1.00

n=1.33

Virtual image

Mon. Feb. 4, 2008 Physics 208, Lecture 4 12

Lens

Object

Image

How do you ‘see’ this?

  Lens bends (refracts) light rays— forms image on retina   Sensors on retina report to brain.

  Color information, intensity information

3

Mon. Feb. 4, 2008 Physics 208, Lecture 4 13

Making a real image   Lens: Refracts light so that rays originating from

a point are focused to a point on the other side.

This is a real image

Mon. Feb. 4, 2008 Physics 208, Lecture 4 14

F

n1

n2>n1

n1

How a lens works Position surfaces to bend light rays in just the right way Spherical surfaces are very close to the right ones.

Optical Axis

Mon. Feb. 4, 2008 Physics 208, Lecture 4 15

1) Rays parallel to optical axis pass through focal point. 2) Rays through center of lens are not refracted. 3) Rays through F emerge parallel to optical axis.

Thin-lens approximation: Ray tracing

F

F

Object

Image Optical Axis

Here image is real, inverted, enlarged

Mon. Feb. 4, 2008 Physics 208, Lecture 4 16

Different object positions

Image (real, inverted)

Image (real, inverted) Object

Image (virtual, upright) These rays seem to originate

from tip of a ‘virtual’ arrow.

Mon. Feb. 4, 2008 Physics 208, Lecture 4 17

Quick Quiz I project a focused image onto a screen 2

meters away. I now want to make the image bigger without changing the lens. I should

A.  Move screen farther away only

B.  Move screen closer only

C.  Move screen closer and object toward lens

D.  Move screen farther and object toward lens

E.  Move screen farther and object away from lens

Mon. Feb. 4, 2008 Physics 208, Lecture 4 18

Making an image

s’ s

Object Image

Image distance Object distance

f f

focal length

How are all these related?

€

1s

+1′ s =1f

4

Mon. Feb. 4, 2008 Physics 208, Lecture 4 19

Lens

Object

Image

Your eye can change focal length

  What is range of focal lengths if it can focus from near point (25 cm) to inf. onto retina 1.7 cm away?

€

1s

+1′ s

=1f

Object at infinity:

€

1∞

+1

1.7cm=1f⇒ f =1.7cm

Object at near point:

€

125cm

+1

1.7cm=1f⇒ f =1.59cm

Very limited range Mon. Feb. 4, 2008 Physics 208, Lecture 4 20

Image size vs object size: Magnification

= M = Magnification

€

image heightobject height

=′ s

s=

image distanceobject distance

Image height

Image distance

Object dist.

Object height

Mon. Feb. 4, 2008 Physics 208, Lecture 4 21

Question

  At what object distance does image size equal object size (magnification=1)?

€

1s

+1′ s =1f

A.  Object distance = f

B.  Object distance = 2f

C.  Object distance = f/2

D. Object distance = infinity

E.  Object distance =0

Mon. Feb. 4, 2008 Physics 208, Lecture 4 22

Different object positions

Image (real, inverted)

Image (real, inverted) Object

Image (virtual, upright) These rays seem to originate

from tip of a ‘virtual’ arrow.

Mon. Feb. 4, 2008 Physics 208, Lecture 4 23

Virtual images

  Virtual image   can’t be recorded on film,   Can’t be seen on a screen.

  But rays can be focused by another lens   e.g. lens in your eye (focus on retina)   e.g. lens in a camera (focus on film plane)

Image (virtual, upright)

These rays seem to originate from tip of a ‘virtual’ arrow.

objects closer to a converging lens than the focal length form a virtual image

Mon. Feb. 4, 2008 Physics 208, Lecture 4 24

  Do these rays come from real image, a virtual image, or an object?

Can’t tell. Rays are exactly equivalent, and can be imaged by a lens in exactly the same way.