Chapter 33: Optics

Wavefronts and Rays •  When light or other electromagnetic waves interact with

systems much larger than the wavelength, it’s a good approximation to •  Neglect the wave nature of light. •  Consider that the light travels in straight lines, called rays, while

in a uniform medium. •  Rays are perpendicular to the wavefronts and the rays’ direction is that of

the wave propagation. •  The ray approximation is also known as geometrical optics.

Reflection •  When light reflects from a surface, the incident and reflected rays

make the same angle with the normal to the surface. •  For smooth surfaces, parallel rays all reflect at the same angle. •  The angles are equal (locally) even for rough surfaces.

•  But because of the roughness, the light comes off in random directions. •  This is called diffuse reflection.

The Plane Mirror

Question •  You would like to buy a full-length mirror which allows

you to see yourself from head to toe. The minimum height of the mirror is A) half your height. B) two-thirds of your height. C) equal to your height. D) depends on distance you stand from mirror

Refraction •  Refraction is the bending of light as it crosses the interface

between two different transparent media. •  Refraction occurs because the wave

speed differs in different media. •  For light, the index of refraction n

describes the speed change. •  The speed of a wave in a medium is

v = c/n. •  The angles of incidence and refraction

are related by Snell’s law: n1 sin ✓1 = n2 sin ✓2

Derivation of Snell’s Law �1

x

= sin ✓1

�2

x

= sin ✓2

�i = �tc/ni

�t c

n1 sin ✓1=

�t c

n2 sin ✓2

n1 sin ✓1 = n2 sin ✓2

�1

sin ✓1=

�2

sin ✓2

Clicker question •  The figure shows the path of a light ray through three

different media. Rank the media in order of their refractive indices.

A.  B.  C.  D. 

1 2 3n n n> >

3 1 2n n n> >

3 2 1n n n> >

2 1 3n n n> >

Example: Sunlight strikes the surface of a lake. A diver sees the Sun at an angle of 42.0° with respect to the vertical. What angle do the Sun’s rays in air make with the vertical?

surface n1 = 1.00; air

n2 = 1.33; water

Normal

42°

Transmitted wave

incident wave

θ1

Example: Sunlight strikes the surface of a lake. A diver sees the Sun at an angle of 42.0° with respect to the vertical. What angle do the Sun’s rays in air make with the vertical?

surface n1 = 1.00; air

n2 = 1.33; water

Normal

42°

Transmitted wave

incident wave

θ1

( ) ( )

°=

=

°=

=

1.638920.0sin

42sin333.1sin00.1sinsin

1

1

1

2211

θ

θ

θ

θθ nn

Question 23.8 Gone Fishin’ I

To shoot a fish with a gun, should you aim directly at the

image, slightly above, or slightly below?

1) aim directly at the image

2) aim slightly above

3) aim slightly below

From:http://www.physicsclassroom.com/class/refrn/Lesson-1/Refraction-and-Sight

Mirages

Total internal reflection •  The angle of incidence for when the angle of refraction is

90° is called the critical angle.

1

2

221

2211

sin

90sinsinsinsin

nn

nnnnn

c

c

=

=°=

=

θ

θ

θθ

•  If the incidence angle is greater than the critical angle, the beam can not refract but is completely reflected

Fiber Optics

Dispersion •  Index of refraction depends on wavelength

•  If a beam of white light is incident on silicate glass (say with θinc=45°) which color bends more (due to refraction)?

1.  blue

2.  yellow

3.  red

4.  all refract the same

Polarization

http://webphysics.davidson.edu/physlet_resources/dav_optics/examples/polarization.html

Polarizers

For unpolarized light: Itransmitted = Iincident < cos

2✓ >=

1

2Iincident

•  Poloroid filter: Electric field does work on electrons along strands of filter, causing E field in that direction to be attenuated

An unpolarized beam of light passes through 2 Polaroid filters oriented at 45o with respect to each other. The intensity of the original beam is Io. What is the intensity of the light coming through both filters?

A: (1/1.4)Io B: (1/2)Io C: (1/4)Io D: (1/8)Io E: None of the above

Io

c

Clicker Question

Unpolarized light, traveling in the direction shown, is incident on polarizer 1. Does any light emerge from polarizer 3?

A.  Yes.

B.  No.

QuickCheck 34.9

Example of Polarized Light: •  Scattering of sunlight:

Example of Polarized Light: •  Reflected light from medium with

higher index of refraction: •  Reflected light is more polarized

with electric field parallel to the surface