Question

Light enters a transparent material from air at 30.0° to the normal. It continues within the material at the angle of refraction of 23.0°. What is the critical angle for total internal reflection when this material is surrounded by air?

Answer 1

The value is
`c = 51.38 ^o`

Step-by-step explanation:

From the question we are told that

The angle of incidence is
`\theta_i = 30^o`

The angle of refraction is
`\theta_r = 23^o`

Generally at the point where the light enters the material , from Snell's law we have that

`n = (sin (\theta_i))/(sin (\theta_(r)))`

Here n is the refractive index of the material

=>
`n = (sin (30))/(sin (23))`

=>
`n = 1.28`

Generally for total internal reflection , the critical angel is evaluated using Snell law as follows

`n = (sin (90))/(sin (c))`

=>
`1.28 * sin (c) = sin(90)`

=>
`c = sin^(-1) [0.7813 ]`

=>
`c = 51.38 ^o`