Question

A beam of light in air enters a glass slab with an index of refraction of 1.40 at an angle of incidence of 30.0°. What is the angle of refraction? (index of refraction of air=1)

Answer 1

Answer:

$\boxed{\sf Angle \: of \: refraction \: (r) = {sin}^{ - 1} ( \frac{1}{2.8} )}$

Given:

Refractive index of air ( $\sf \mu_{air}$ )= 1

Refractive index of glass slab ( $\sf \mu_{glass}$) = 1.40

Angle of incidence (i) = 30.0°

To Find:

Angle of refraction (r)

Explanation:

From Snell's Law:

$\boxed{ \bold{ \sf \mu_{air}sin \ i = \mu_{glass}sin \: r}}$

$\sf \implies 1 \times sin \: 30 ^ \circ = 1.4sin \:r$

$\sf sin \:30^ \circ = \frac{1}{2} :$

$\sf \implies \frac{1}{2} = 1.4 sin \: r$

$\sf \frac{1}{2} = 1.4 sin \: r \: is \: equivalent \: to \: 1.4 sin \: r = \frac{1}{2} :$

$\sf \implies 1.4 sin \: r = \frac{1}{2}$

Dividing both sides by 1.4:

$\sf \implies \frac{\cancel{1.4} sin \: r}{\cancel{1.4}} = \frac{1}{2 \times 1.4}$

$\sf \implies sin \: r = \frac{1}{2 \times 1.4}$

$\sf \implies sin \: r = \frac{1}{2.8}$

$\sf \implies r = {sin}^{ - 1} ( \frac{1}{2.8} )$

$\therefore$

$\sf Angle \: of \: refraction \: (r) = {sin}^{ - 1} ( \frac{1}{2.8} )$