Chapter 22

Chapter 22

Reflection and Refractionof

Light

Law of reflection and refraction The incident ray, the

normal and the reflected ray are coplanar.

θ 1 = θ1’ n1 sin θ1 = n2 sin θ2

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

Variation of Index of Refraction with Wavelength

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

Violet light refracts more than red light when passing from air into a material

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

Red deviates the least

Prism Spectrometer

A prism spectrometer uses a prism to cause the wavelengths to separate

The instrument is commonly used to study wavelengths emitted by a light source

Using Spectra to Identify Gases All hot, low pressure gases emit their

own characteristic spectra The particular wavelengths emitted by a

gas serve as “fingerprints” of that gas Some uses of spectral analysis

Identification of molecules Identification of elements in distant stars Identification of minerals

The Rainbow A ray of light strikes a drop of

water in the atmosphere It undergoes both reflection and

refraction First refraction at the front of the drop

Violet light will deviate the most Red light will deviate the least

The Rainbow, 2 At the back surface the

light is reflected It is refracted again as it

returns to the front surface and moves into the air

The rays leave the drop at various angles

The angle between the white light and the violet ray is 40°

The angle between the white light and the red ray is 42°

Observing 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

12

Rainbows

33-Fig. 33-22

Sunlight consists of all visible colors and water is dispersive, so when sunlight is refracted as it enters water droplets, is reflected off the back surface, and again is refracted as it exits the water drops, the range of angles for the exiting ray will depend on the color of the ray. Since blue is refracted more strongly than red, only droplets that are closer the the rainbow center (A) will refract/reflect blue light to the observer (O). Droplets at larger angles will still refract/reflect red light to the observer.What happens for rays that reflect twice

off the back surfaces of the droplets?

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

incidence is called the critical angle

21 2

1sin C

n for n nn

Critical Angle, cont 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 Total internal reflection occurs only

when light attempts to move from a medium of higher index of refraction to a medium of lower index of refraction

Fiber Optics An application of

internal reflection Plastic or glass rods

are used to “pipe” light from one place to another

Applications include Medical use of fiber

optic cables for diagnosis and correction of medical problems

Telecommunications

R > nd/(n-1)

Solution 22.52

(a) A ray originally traveling along the inner edge will have the smallest angle of incidence when it strikes the outer edge of the fiber in the curve. Thus, if this ray is totally internally refl ected,all of the others are also totally reflected. For this ray to be totally internally reflected it is necessary that θ≥θc or sinθ≥sinθc = 1/But, sinθ = (R-d)/R, so we must have (R –d)/R ≥ 1/nwhich simplifies to R ≥ nd /(n−1)

(b) As d→0, R→0. This is reasonable behavior.As n increases, Rmin = nd/(n-1) = d/(1-1/n) decreases. This is reasonable behavior.As n→1, Rmin increases. This is reasonable behavior.

(c) Rmin = nd/(n-1) = 1.4x100μm/(1.4-1) = 350 μm

What is the index of refraction?

22.20

22.20

Since the light ray strikes the first surface at normal incidence, it passes into the prism without deviation. Thus, the angle of incidence at the second surface (hypotenuse of the triangular prism) is θ1=45.0°, as shown in the sketch at the right. The angle of refraction is θ2 =45.0°+15.0°=60.0° and Snell’s law gives the index of refraction of the prism material as

n2 = n1 sinθ1/ sin θ2 = 1 sin 60/sin 45 = 1.22

20.49

What is θ4 ? n2 is increased, at what

value of n2 the light beam goes straight through?

20.49 solution

θ1 = 60 = θ2 θ3 +90 +30+30 = 180 => θ3 = 30n1 sin 30 = sinθ4

θ4 = 38.5 n2 > n1 sin 60 = (1.66) sin60 = 1.44