Chapter 30

Reflection and Refraction

Geometric Optics and Ray Approximation

• Light travels in a straight-line path in a homogeneous medium until it encounters a boundary between two different media

• The ray approximation is used to represent beams of light – a ray of light is an imaginary line drawn along the direction of travel of the light beams

• A wave front is a surface passing through points of a wave that have the same phase

• The rays, corresponding to the direction of the wave motion, are perpendicular to the wave front

• Light travels in a straight-line path in a homogeneous medium until it encounters a boundary between two different media

• The ray approximation is used to represent beams of light – a ray of light is an imaginary line drawn along the direction of travel of the light beams

• A wave front is a surface passing through points of a wave that have the same phase

• The rays, corresponding to the direction of the wave motion, are perpendicular to the wave front

Geometric Optics and Ray Approximation

Specular Reflection

• Specular reflection is reflection from a smooth surface

• The reflected rays are parallel to each other

• All reflection in this chapter is assumed to be specular

Diffuse Reflection

• Diffuse reflection is reflection from a rough surface

• The reflected rays travel in a variety of directions

• Diffuse reflection makes the dry road easy to see at night

Law of Reflection• The normal is a line perpendicular

to the surface at the point where the incident ray strikes the surface

• The incident ray makes an angle of θ1 with the normal and the reflected ray makes an angle of θ1’ with the normal

• The angle of reflection is equal to the angle of incidence:

θ1= θ1’

Refraction of Light

• When a ray of light traveling through a transparent medium encounters a boundary leading into another transparent medium, part of the ray is reflected and part of the ray enters the second medium

• The ray that enters the second medium is refracted – bent at the boundary

Refraction of Light

• The incident ray, the reflected ray, the refracted ray, and the normal all lie on the same plane

• The angle of refraction, θ2, depends on the properties of the medium and the angle of incidence

• The path of the light through the refracting surface is reversible

constv

v

1

2

1

2

sin

sin

Refraction of Light

• Ray is the incident ray

• Ray is the reflected ray

• Ray is refracted into the crystal

• Ray is internally reflected in the crystal

• Ray is refracted as it enters the air from the crystal

Refraction of Light

• Light may refract into a material where its speed is lower

• The angle of refraction is less than the angle of incidence so the ray bends toward the normal

constv

v

1

2

1

2

sin

sin

Refraction of Light

• Light may refract into a material where its speed is higher

• The angle of refraction is greater than the angle of incidence so the ray bends away from the normal

constv

v

1

2

1

2

sin

sin

The Index of Refraction• When light passes from one medium to another, it is

refracted because the speed of light is different in the two media

• The index of refraction, n, of a medium can be defined

• n is a unitless ratio

• For a vacuum, n = 1 whereas for other media, n > 1

speed ofl ight in a vacuum cn

speed ofl ight in a medium v

The Index of Refraction

• The wavefronts do not pile up, nor are created or destroyed at the boundary

• Therefore, as light travels from one medium to another, its frequency does not change

• Both the wave speed and the wavelength do change

The Index of Refraction

v1 = ƒ λ1 v2 = ƒ λ2

• The ratio of the indices of refraction of the two media can be expressed as various ratios

1 1 1 2

2 2 12

cv n n

cv nn

Snell’s Law of Refraction

n1 sin θ1 = n2 sin θ2

1 1 1 2

2 2 12

cv n n

cv nn

Willebrord Snelvan Royen

1580 – 1626

1

2

1

2

sin

sin

v

v

2

2

1

1

sinsin

Chapter 30Problem 35

You’re standing 2.3 m horizontally from the edge of a 4.5-m-deep lake, with your eyes 1.7 m above the water’s surface. A diver holding a flashlight at the lake bottom shines the light so you can see it. If the light in the water makes a 42° angle with the vertical, at what horizontal distance is the diver from the edge of the lake?

Atmospheric Refraction• There are many interesting results

of refraction in the atmosphere

• At sunsets, light rays from the sun are bent as they pass into the atmosphere

• It is a gradual bend because the light passes through layers of the atmosphere, and each layer has a slightly different index of refraction

• The Sun is seen to be above the horizon even after it has fallen below

Atmospheric Refraction• A mirage can be observed when the air above the

ground is warmer than the air at higher elevations

• The rays in path B are directed toward the ground and then bent by refraction

• The observer sees both an upright and an inverted image

Atmospheric Refraction

Polarization by Reflection

• When an unpolarized light beam is reflected from a surface, the reflected light can be completely polarized, partially polarized, or unpolarized

• It depends on the angle of incidence

• If the angle is 0° or 90°, the reflected beam is unpolarized

• For angles between this, there is some degree of polarization

• For one particular angle, the beam is completely polarized

Polarization by Reflection

• The angle of incidence for which the reflected beam is completely polarized is called the polarizing (or Brewster’s) angle, θp

• Brewster’s Law relates the polarizing angle to the index of refraction for the material

sintan

cosp

pp

n

Sir David Brewster

1781 – 1868

18090 2 p p 902

2

1

sin

sin

n2sin

sin

p

p

p

cos

sin

Total Internal Reflection

• Total internal reflection can occur when light attempts to move from a medium with a high index of refraction to one with a lower index of refraction

• Ray 5 shows internal reflection

Critical Angle• A particular angle of incidence (critical

angle) will result in an angle of refraction of 90°

• For angles of incidence greater than the critical angle, the beam is entirely reflected at the boundary

• This ray obeys the Law of Reflection at the boundary

21 2

1

sin C

nfor n n

n

Chapter 30Problem 48

Find a simple expression for the speed of light in a material in terms of c and the critical angle at an interface between the material and vacuum.

Fiber Optics

• Utilizes internal reflection

• Plastic or glass rods are used to “pipe” light from one place to another

• Applications include diagnosis and correction of medical problems, telecommunications, etc.

Dispersion• The index of refraction in anything except

a vacuum depends on the wavelength of the light

• This dependence of n on λ is called dispersion

• Snell’s Law indicates that the angle of refraction made when light enters a material depends on the wavelength of the light

• The index of refraction for a material usually decreases with increasing wavelength

Refraction in a Prism• The amount the ray is bent away from its original

direction is called the angle of deviation, δ

• Since all the colors have different angles of deviation, they will spread out into a spectrum: violet deviates the most and red deviates the least

Spectroscopy

• A prism spectrometer uses a prism to cause the wavelengths to separate (to study wavelengths emitted by a light source)

• All hot, low pressure gases emit their own characteristic spectra with the particular wavelengths emitted by a gas serving as “fingerprints” of that gas

• Spectral analysis: identification of molecules, minerals, elements in distant stars, etc.

The Rainbow• A ray of light strikes a drop of water

in the atmosphere and undergoes both reflection and refraction

• First refraction at the front of the drop: violet light will deviate the most and red – the least

• At the back surface the light is reflected and refracted again as it returns to the front surface and moves into the air

• The rays leave the drop at various angles

The Rainbow• If a raindrop high in the sky is observed, the red ray is

seen

• A drop lower in the sky would direct violet light to the observer

• The other colors of the spectra lie in between the red and the violet

Answers to Even Numbered Problems

Chapter 30:

Problem 12

(a) 4

Answers to Even Numbered Problems

Chapter 30:

Problem 36

1.3 m

Answers to Even Numbered Problems

Chapter 30:

Problem 38

42°