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A ray of light is travelling from a denser medium to a rarer medium. For these media, the critical angle is C. The maximum possible deviation of the ray is ______. [Hint: the situation at total reflection is shown in the figure.]

Asked in RS Academy GUJCET booklet · Total internal reflection and optical fibres

Figure: Total internal reflection and optical fibres
Answer: (2) π-2C

Step-by-step solution

Given: light going from a denser to a rarer medium, with critical angle C.

Idea: two things can happen, and the maximum deviation has to be found over both.

For i<C the ray refracts and bends away from the normal, so it is deviated by r-i. This grows with i and is largest just at i=C, where r=90°: the deviation there is π/2-C.

For i≥ C the ray is totally reflected, and a reflected ray is turned through π-2i from its original direction.

That expression is largest at the smallest allowed i, which is i=C, giving π-2C.

Comparing the two regimes, π-2C is greater than π/2-C whenever C<90°, so the maximum possible deviation is π-2C and it happens exactly at the critical angle.

Why the other options are wrong

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