Use the exact values you enter to make later calculations. A ray of light strike

Question

Use the exact values you enter to make later calculations.

A ray of light strikes a flat, 2.00-cm-thick block of glass (n = 1.38) at an angle of = 32.6° with respect to the normal (see figure below).

(a) Find the angle of refraction at the top surface and the angle of incidence at the bottom surface.
°

(b) Find the refracted angle at the bottom surface.
°

(c) Find the lateral distance d by which the light beam is shifted.
cm

(d) Calculate the speed of light in the glass.
m/s

(e) Calculate the time required for the light to pass through the glass block.
s

Explanation / Answer

a)

angle of refraction at the top surface and the angle of incidence at bottom surface is same

using snell's law

n1*sin(i) = n2*sin(r)

1*sin(32.6) = 1.38*sin(r)

sin(32.6)/1.38 = sin(r)

0.39 = sin(r)

r = sin^(-1)(0.39) = 23 deg

angle of refraction at the top surface is r = 23 deg

the angle of incidence at bottom surface is 23 deg

b) again using snell's law

n2*sin(i2) = n3*sin(r2)

1.38*sin(23) = 1*sin(r2)

r2 = sin^(-1)(0.54) = 32.68 deg

c) d = AB*sin(32.68)

AB = 2/cos(23) = 2.17 cm

then

d = 2.17*sin(32.68) =1.17 cm

d) speed of light is v = c/n = (3*10^8)/1.38 = 2.17*10^8 m/s

e) time t = AB/v = 2.17*10^-2/(2.17*10^8) = 1*10^-10 sec

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