Question

A glass plate whose index of refraction is 1.64 is immersed in a liquid. The surface of the glass is inclined at an angle of 47° with the vertical. A horizontal ray in the glass is incident on the interface. When the liquid is a certain alcohol, the incident ray arrives at the interface at the critical angle. The index of refraction of the alcohol is closest to:

Answer 1

nr = 1.1994

Step-by-step explanation:

Critical is the angle at which if increased beyond will cause total internal reflection and total internal reflection only occurs when light is traveling from denser medium to a less dense medium

The formula for critical angle

sin C = nr /ni where ni is the refractive index of the glass and nr is the refractive index of the certain alcohol and C is the critical angle = 47°, ni = 1.64

substitute the values into the expression

ni sin C = nr

1.64 × sin 47

nr = 1.1994