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Question

For the given incident ray as shown in figure, the condition of total refraction of this ray the minimum refractive index of prism will be :
1452673_cf71988311234734860fe4eba063f9ed.png

A
3+12
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B
2+12
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C
52
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D
72
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Solution

The correct option is C 52
From ΔBCD we have
ic+r+90=180
r=90ic
μ=sinisinr=sin30sinr=sin30sin(90ic)=1/2cosic
We know that
μ=1sinic
1/2cosic=1sinic
tanic=2
Placing this in a triangle we get p=2,b=1
Hence h=22+1=5
sinic=25
Hence, μ=52
Therefore the correct answer is option (C).


1998413_1452673_ans_986d543085fb449c8913b35125bddbaa.JPG

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