A point source of light is submerged 2.8 m below the surface of a lake and emits

Question

A point source of light is submerged 2.8 m below the surface of a lake and emits rays in all directions. On the surface of the lake, directly above the source, the area is a circle. What is the maximum radius that this circle could have? 3.18 m The drawing shows a crystalline quartz slab with a rectangular cross section. A ray of light strikes the slab at an incident angle of theta_1 = 32 degree., enters the quartz, and travels to point P. slab is surrounded by a fluid with a refractive index n. What is the maximum value of n such that total internal reflection occurs at point P? ) = 1.544) 1.170

Explanation / Answer

theta1 = 32 deg ; n = 1.544

from Snell's law,

n1 sin(theta1) = n2 sin(theta2) (1)

At point P,

n2 sin(theta2) = n3 sin(theta3)

n2 sin(90 - theta2) >= sin90

n2 cos(theta2) >= n1

n1 = n(max) = n2 cos(theta2) (2)

(1)/(2)

sin(theta1) = tan(theta2)

theta2 = tan-1 [sin(theta1)] = tan -1 [sin32] = 27.92 deg

n(max) = n2 cos(theta2)

n(max) = 1.544 x cos27.92 = 1.364

Hence, n(max) = 1.364

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