Question

A glass plate having an index of refraction is 1.66 is immersed in a certain alcohol. The surface of the glass is inclined at an angle of 44° with the vertical. When a horizontal ray in the glass strikes the interface, you observe that it is at the critical angle. What is the index of refraction of the alcohol?

Answer 1

1.153

Step-by-step explanation:

Refractive index of glass with respect to alccohol

=
`(refractive index of glass)/(refractive index of alcohol)`

=
`(1.66)/(x)`

Refractive index of glass with respective respect to alcohol

=
`(1)/(\sin C)`

Critical angle C is angle made in denser medium by ray of light with the vertical on the surface. In this case it is 44 degree.

So ,
`(1)/(\sin C)` =
`(1.66)/(x)`

x = 1.66 \times \sin44

= 1.66 x 0.694

=1.153