You have a beaker with a mystery liquid at the bottom and a layer of water over

Question

You have a beaker with a mystery liquid at the bottom and a layer of water over it. You shine a laser up through the BOTTOM of the beaker with the laser light encountering the mystery liquid to water transition with the path of the light and angles shown below (there is no typo in the labeling of the angles - use what you are given and knowledge of geometry to find the answer). The index of refraction for both water and air are in your textbook if you don’t remember them from class.

A) Find the index of refraction of the mystery liquid X at the bottom of the beaker.

B) Find the angle the light makes with the normal (the angle of transmission) when it refracts as it passes from the water into the air.

Explanation / Answer

here,

refractive index of air , n1 = 1

refractive index of water , n2 = 1.33

let the refractive index of liquid be nx

(a)

using snell's law

sin(54)/sin(90 - 65) = nx /n2

sin(54)/sin(90 - 65) = nx /1.33

nx = 2.55

the refractive index of the liquid is 2.55

(b)

the angle the light makes with normal be i

using the snell's law

sin(i)/sin(45) = 1.33/1

i = 72.13 degree

the angle the light makes with the normal when it refracts as it passes from the water into the air is 72.13 degree

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