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

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

Step-by-step explanation:

From Snell's Law:

`\boxed{ \bold{ \sf \mu_(air)sin \ i = \mu_(glass)sin \: r}}`

`\sf \implies 1 * sin \: 30 ^ \circ = 1.4sin \:r`

`\sf sin \:30^ \circ = (1)/(2) :`

`\sf \implies (1)/(2) = 1.4 sin \: r`

`\sf (1)/(2) = 1.4 sin \: r \: is \: equivalent \: to \: 1.4 sin \: r = (1)/(2) :`

`\sf \implies 1.4 sin \: r = (1)/(2)`

Dividing both sides by 1.4:

`\sf \implies \frac{\cancel{1.4} sin \: r}{\cancel{1.4}} = (1)/(2 * 1.4)`

`\sf \implies sin \: r = (1)/(2 * 1.4)`

`\sf \implies sin \: r = (1)/(2.8)`

`\sf \implies r = {sin}^( - 1) ( (1)/(2.8) )`

`\therefore`

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