Lecture 13Dispersion and Internal Reflection

Chapter 22.5 22.8

Outline

• Dispersion of Light• Huygens Principle• Total Internal Reflection

Dispersion of Light

The index of refraction n depends on the wavelength of light in any medium, except for vacuum.

This phenomenon is called dispersion.

c speed of light in vacuumn = v speed of light in a medium

According to Snell’s law, the angle of refraction of light depends on its wavelength.

n1 sin 1 = n2 sin 2

Dispersion of LightPropagation of light through a prism.

Picture

A ray of light of a single wavelength entering the prism bents away from its original direction by an angle (deviation angle).Light of different wavelengths (colors) will bend (refract) by different angles.The rays, emerging from the prism, will spread out in a series of color (spectrum).

Huygens’ Principle

Huygens assumed that light is a form of wave motion.

Huygens’ principle allow to determine the position of a new wave front from the knowledge of a preceding one.

The Principle: all points on a wave front are considered point sources for production of spherical secondary waves (wavelets), which propagate in the forward direction with speeds, characteristic of waves in the medium. The new position of the wave front is the surface tangent to the wavelets.

Rainbow

Formation of a rainbow Variety

Total Internal Reflection

Light moving from a higher index of refraction medium to one with a lower index of refraction may experience total internal reflection.

A some angle of incidence c (critical angle) the refracted light will move parallel to the boundary.The refraction angle is 90o in this case.For water (n=1.33), sin c = 1/1.33, and c = 48.8o

For angles of incidence greater than c , the beam is entirely reflected at the boundary.

Problem on Total Internal ReflectionProblem: A small underwater pool light is 1 m below the surface. What is the radius of the surface, from which light emerges from the water?

nW = 1.33 sin c = 1/1.33

cd = 1 m

R

R/d = tan c

nW sin c = 1

R = 1.14 m

c = 48.8o

Summary

• Dispersion of light is dependence of the index of refraction on the wavelength

• Huygens’ principle is a geometrical approach to find the new position of a wave front, assuming that all points on a preceding wave front produce secondary spherical waves (wavelets).

• Total internal reflection occurs only when light moves from a medium with a higher index of refraction to one with a lower index of refraction.