A beam of light is emitted in a pool of water (n = 1.33) from a depth of 61.0 cm

Question

A beam of light is emitted in a pool of water (n = 1.33) from a depth of 61.0 cm. The light ray strikes the surface a horizontal distance x from the spot directly above the light source as shown in the diagram below. For air, the index of refraction is n_air =1. SHOW WORK. Suppose the beam strikes the water - air surface a horizontal distance 112.5 cm from the spot directly above the light source. Will the light exit the water ? Answer yes or no. If yes, give the angle the beam makes with the normal after it exits the water into the air (n_air =1). Diagram the problem in the white spaces below. Suppose the beam strikes the water - air surface a horizontal distance 45.7 cm from the spot directly above the light source. Will the light exit the water ? Answer yes or no. If yes, give the angle the beam makes with the normal after it exits the water into the air (n_air =1). Diagram the problem in the white spaces below.

Explanation / Answer

According to the given problem,

2) First, find the critical angle for the light leaving the water,

nwaterSinc = nairSin90°

Sinc = 1/1.33

c = 48.8°

From the diagram,

Tanc= x/61.0

x = 69.7 cm[horizontal distance]

a) No, Reason: if a light is incident at a greater angle that c[critical angle] it will totally reflect so, x > H* Tanc

As 112.5 > 69.7 [Total internal reflection]

b) Yes, Reason: if a light is incident at a greater angle that  c[critical angle] it will totally reflect so, x > H* Tanc

As 45.7 < 69.7 [NO, Total internal reflection]

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