Question

Chapter 26, Problem 027 A glass is half-full of water, with a layer of oil (n = 1.46) floating on top. A ray of light traveling downward through the oil is incident on the water at an angle of 73.7°. Take the refractive index of water to be 1.333. (a) Determine the critical angle for the oil-water interface. (b) Will the ray penetrate into the water

Answer 1

a) angle is 65.63 degree

b) Ray cannot be penetrate. it will reflect form oi and water surface

Step-by-step explanation:

Refractive index for oil ,
`n_1 = 1.46`

and Refractive index for water,
`n_2 = 1.333`

when light passes from oil to water then we have following relation

`n_1*  sin i = n_2 * sin r`

For i = critical angle, r is 90 degree

therefore

`n_1. sin c = n_2`

`sin c = (n_2)/(n_1)`

`c =sin^(-1) (1.33)/(1.46) = 65.63 degree`

the angle of incidence is i 73.7 which is greater than 65.63 therefore , ray cannot be penetrate. it will reflect form oi and water surface