Question

A beam of light strikes a sheet of glass at an angle of 56.6° with the normal in air. You observe that red light makes an angle of 38.4° with the normal in the glass, while violet light makes a 36.4° degree angle.
1.What are the indexes of refraction of this glass for these colors of light?

2.What are the speeds of red and violet light in the glass?

Answer 1

Answer:

(a). Index of refraction are $n_{red}$ = 1.344 & $n_{violet}$ = 1.406

(b). The velocity of red light in the glass $v_{red} =$ 2.23 ×$10^{8} \ \frac{m}{s}$

The velocity of violet light in the glass $v_{violet} =$2.13 ×$10^{8} \ \frac{m}{s}$

Explanation:

We know that

Law of reflection is

$n_1 \sin\theta_{1} = n_2 \sin\theta_{2}$

Here

$\theta_1$ = angle of incidence

$\theta_2$ = angle of refraction

(a). For red light

1 × $\sin 56.6$ = $n_{red}$ × $\sin 38.4$

$n_{red}$ = 1.344

For violet light

1 × $\sin 56.6$ = $n_{violet}$ × $\sin 36.4$

$n_{violet}$ = 1.406

(b). Index of refraction is given by

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

$n_{red}$ = 1.344

$v_{red} = \frac{c}{n_{red} }$

$v_{red} = \frac{3(10^{8} )}{1.344}$

$v_{red} =$ 2.23 ×$10^{8} \ \frac{m}{s}$

This is the velocity of red light in the glass.

The velocity of violet light in the glass is given by

$v_{violet} = \frac{3(10^{8} )}{1.406}$

$v_{violet} =$2.13 ×$10^{8} \ \frac{m}{s}$

This is the velocity of violet light in the glass.