Question

A beam of light strikes a sheet of glass at an angle of 57.0°. with the normal in air. You observe that red light makes an angle of 38.1° with the normal in the glass, while violet light makes a 36.7° angle.
a. What are the indexes of refraction of this glass for these colors of light?
b. What are the speeds of red and violet light in the glass?

Answer 1

Answer:

a) Red: 1.34

Violet: 1.40

b) Red: $2.23\times10^8\frac{m}{s}$

Violet: $2.14\times10^8\frac{m}{s}$

Explanation:

a) We should use Snell's law to find the index of refraction:

$n_{1}sin\theta_{i}=n_{2}sin\theta_{t}$

with n1 the index of refraction of air, n2 the index of refraction of the glass, θi the angle of the incident ray respects the normal an θt the angle between the refracted ray an the normal. It's common to approximate n1=1

solving n2 for red light:

$\frac{sin\theta_{i}}{sin\theta_{t}}=n_{2}$

$n_2=\frac{sin57.0}{sin38.1}= 1.34$

solving n2 for violet light:

$\frac{sin\theta_{i}}{sin\theta_{t}}=n_{2}$

$n_2=\frac{sin57.0}{sin36.7}= 1.40$

b) Index of refraction on a medium is defined as the ratio between the velocity of electromagnetic waves on vacuum (velocity of light c) and the velocity in medium (v):

$n_2=\frac{c}{v}$

solving v for red:

$v=\frac{c}{n_2}=\frac{3\times10^8}{1.34}=2.23\times10^8\frac{m}{s}$

solving v for violet

$v=\frac{c}{n_2}=\frac{3\times10^8}{1.40}=2.14\times10^8\frac{m}{s}$