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:

Question

Wayne Cummings

Physics

3 September, 21:32

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:

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Answers (1)

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Jon Reilly · Answer 1

nr = 1.1994

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