A glass hemisphere is completely submerged in a fluid. When a beam of light is i

Question

A glass hemisphere is completely submerged in a fluid. When a beam of light is incident upon the flat glass surface, the light is refracted with the angles shown. The angles are:

1=52.71=52.7

2=602=60

If the speed of light in the fluid is 0.724c, what is the index of refraction of the glass?

And the beam of light enters the flat surface at the exact center of the glass hemisphere and exits the glass at the point P. What is the angle of refraction as the light enters the fluid at P?

1. 1

2. 2

3. 901

4. 902

5. 0.0

6. 90

7. total internal reflection occurs at point P, so the light does not enter the fluid

Explanation / Answer

given, speed of light in fluid = 0.724 c
hence refractive index of fluid nf = c/0.724c = 1.3812
now, given, phi1 = 52.7 deg
phi2 = 60 deg
hence
from snell's law
sin(phi1)/sin(phi2) = n/nf ( wehre n is refractive index of glass)
sin(52.7)/sin(60) = n/1.3812
n = 1.268

angle of refraction as light enters through center of hemisphere = phi2
angle of refraction at point P = 0deg ( as light coming from the centger pf the hemisphere is normal to the surface of hemisphere)

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