Chapter 22 Reflection and Refraction of Light

Law of reflection and refraction The incident ray, the normal and the reflected ray are coplanar. θ 1 = θ 1 ’ n 1 sin θ 1 = n 2 sin θ 2

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 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

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 (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≥θ c or sinθ≥sinθ c = 1/ But, sinθ = (R-d)/R, so we must have (R –d)/R ≥ 1/n which simplifies to R ≥ nd /(n−1) (b) As d→0, R→0. This is reasonable behavior. As n increases, R min = nd/(n-1) = d/(1-1/n) decreases. This is reasonable behavior. As n→1, R min increases. This is reasonable behavior. (c) R min = nd/(n-1) = 1.4x100μm/(1.4-1) = 350 μm

What is the index of refraction? 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 θ 1 =45.0°, as shown in the sketch at the right. The angle of refraction is θ 2 =45.0°+15.0°=60.0° and Snell’s law gives the index of refraction of the prism material as n 2 = n 1 sin θ 1 / sin θ 2 = 1 sin 60/sin 45 = 1.22

20.49 What is θ 4 ? n 2 is increased, at what value of n 2 the light beam goes straight through?

20.49 solution θ 1 = 60 = θ 2 θ = 180 => θ 3 = 30 n 1 sin 30 = sinθ 4 θ 4 = 38.5 n 2 > n 1 sin 60 = (1.66) sin60 = 1.44