Three transparent media are stacked in the order A–B–C

PHYSICS · Multi-part · A Level · Physics · Waves · Waves

Problem

Three transparent media are stacked in the order A–B–C, all interfaces being parallel planes. Their indices of refraction satisfy

n_{\text{A}}<n_{\text{B}}

and

n_{\text{C}}<n_{\text{B}}

. A light ray in medium A is incident on the A–B interface at an angle

\theta_{\text{i}}

relative to the normal. (1) Derive an expression for the critical angle

\theta_{\text{c}}

at the B–C interface in terms of

n_{\text{B}}

and

n_{\text{C}}

. Clearly state the physical meaning of the critical angle. (2) Using your result from part (a), determine an inequality that

\theta_{\text{i}}

must satisfy to guarantee that the ray ultimately refracts into medium C rather than undergoing total internal reflection at the B–C interface. Express your answer in terms of

n_{\text{A}},\, n_{\text{B}},

and

n_{\text{C}}

. Provide a concise justification. (3) Describe qualitatively what happens to the path of the light ray as

\theta_{\text{i}}

is gradually increased from small values to angles that violate the inequality found in part (b). Emphasize changes in the number and nature (refracted vs. reflected) of rays at each interface.

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