Question

A ray of light is traveling in glass and strikes a glass/liquid interface. The angle of incidence is 58.0°, and the index of refraction of glass is n = 1.50.

(a) What must be the index of refraction of the liquid such that the direction of the light entering the liquid is not changed?

(b) What is the largest index of refraction that the liquid can have, so that none of the light is transmitted into the liquid and all of it is reflected back into the glass?

Answer 1

Part A.

Given that direction of light entering the liquid should not be changed, So that means there should be no refraction, OR angle of incidence = angle of refraction

Usin snell's law:

n1*sin i = n2*sin r

since sin i = sin r, So

n1 = n2

n1 = refractive index of glass

n2 = refractive index of liquid

So, n2 = 1.50 = refractive index of liquid for no direction change

Part B.

Now given that none of the light should be transmitted into the liquid and all of it is reflected back into the glass, So that means there should be total internal reflection in glass medium, that means 58 deg will be critical for TIR

So again using snell's law:

n1*sin i = n2*sin r

r = angle of refraction = 90 deg

i = angle of incidence = critical angle = 58 deg

n1 = 1.50

So,

n2 = n1*sin i/sin r

n2 = 1.50*sin 58.0 deg/sin 90 deg

n2 = refractive index of liquid medium = 1.27

Let me know if you've any query.