A ray of light is passing through air(n=1). It strikes a level surface of water

Question

A ray of light is passing through air(n=1). It strikes a level surface of water (n=1.33) at an angle of 40degree with respect to the surface of the water. The water is 10 cm thick. The light ray refracts and travels through the water. There is a level layer of clear polystyrene (n = 1.6) that the water is resting upon. The light ray hits the polystyrene level and travels through it, finally reaching a sheet of glass (n=1.45). Given that the speed of light in a vacuum is 3*10^8 m/s, calculate the speed of light in the water and the time it takes for the light to traverse the water layer. Calculate the critical angle for total internal reflection at the polystyrene-glass interface. Does the light ray enter the glass? If so, at what angle with respect to the normal does the light ray pass through the glass?

Explanation / Answer

a)
v = c/n
= (3*10^8)/1.33
= 2.26*10^8 m/s
Answer: 2.26*10^8 m/s

b)
for critical angle, angle of refraction should be 90 degree

Use Snell's law:
n1*sin i = n2*sin r
1.6* sin i = 1.45* sin 90
i = 65 degree
Answer: 65 degree

c)
Find angle of incidence in polysterene
1*sin 40 = 1.6* sin r
r= 22 degree

for polysterene - glass interference,
i = 90 -22 = 68 degree

so Total internal reflection will take place

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