Consider a light ray traveling between air and a diamond cut in the shape shown

Question

Consider a light ray traveling between air and a diamond cut in the shape shown in the figure. Refractive index values: air, 1.000; water, 1.333; diamond, 2.419

(a) Calculate the critical angle for total internal reflection of light traveling in diamond and incident on a diamond-air interface.

(b) Consider the light ray incident normally on the top surface of the diamond as shown in the figure. Show by calculation that the light traveling toward point P is totally reflected.

(c) If the diamond is immersed in water, calculate the critical angle at the diamond-water interface.

(d) When the diamond is immersed in water, does the light ray incident normally on the top surface of the diamond undergoes total reflection at point P? Explain.

Explanation / Answer

a) Apply, Snell's law

sin(theta_i)/sin(theta_r) = n2/n1

when, theta_r = 90 degrees, theta_i = theta_c

sin(theta_c)/sin(90) = 1/2.419

theta_c = sin^-1(1/2.419)

= 24.4 degrees

b) from figure, at point P,

theta_i = 35 degrees

here, theta_i > theta_c (24.4 degrees)

so, light will be totally reflected.

c) Apply, Snell's law

sin(theta_i)/sin(theta_r) = n2/n1

when, theta_r = 90 degrees, theta_i = theta_c

sin(theta_c)/sin(90) = 1.333/2.419

theta_c = sin^-1(1.333/2.419)

= 33.4 degrees

d) yes, since theta_i(35 degrees) > theta_c (33.4 degrees)

e) clockwise.

because as we rotate the diamond clockwise direction, angle of incidence(theta_i) value decreases.

when theta_i < theta_c, the light ray will exit through the diamond.

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