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Light is incident along the normal on face AB of a glass prism of refractive index 1.52, as

shown. Find the largest value the angle a can have without any light refracted out of the

prism at face AC if

(a) the prism is immersed in air, and

(b) the prism is immersed in water.

Edit
Added Mon, 16 Nov '15
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From the picture we see that theta_c = 90 - alpha.

Thus, alpha = 90 - theta_c

Recall sin(theta_c) = n_2 / n_1

thus, theta_c = arcsin(n_2/n_1)

(a)

alpha = 90 - arcsin(n_2/n_1)

= 90 - arcsin(1 / 1.52)

= 90 - 41.14

= 48.86 degrees

(b)

alpha = 90 - arcsin(n_2/n_1)

= 90 - arcsin(1.33 / 1.52)

= 90 - 61.044

= 28.95 degrees

Edit
Added Mon, 16 Nov '15
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