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Question

In the figure shown below, find the minimum value of i for which total internal reflection never takes place at P.
[Medium surrounding the slab has refractive index μ2]


A
cos1(1817)
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B
sin1(817)
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C
cos1(178)
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D
sin1(178)
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Solution

The correct option is D sin1(178)
For no total internal reflection at P:
βθc
In critical case, β=θc


So, r=90β=90θc....(1)

We know ,
sinθc=μ2μ1

sinθc=4332=89 ............(2)

Applying snell's law at point Q

μ2sini=μ1sinr

Substituting the given data we get,

43sini=32sin(90θc) [ From (1) ]

89sini=cosθc

89sini=1sin2θc

89sini=16481 [ From (2) ]
89sini=179
sini =178
i=sin1(178)

Hence, option (d) is the correct answer.
Why this question?
This question check your ability to apply geometry and trigonometry in the Snell's law to get the required data.
Such questions are generally asked in JEE Main.


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