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Question

# In fig For an angle of incidence 45∘ at top surface what is the minimum refractive index needed for total internal reflection at vertical face AD?√1/2√2√3/2√2+12

A
2+12
B
1/2
C
2
D
3/2
Solution
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#### The correct option is C√3/2AT point of A by snell'sμ=sin450sinr⇒sinr=1μ√2..........(1)From figure,i1=90−r∴sin(900−r)=1μNow,⇒cosr=1μ..........(2)cosr=√1−sin2r=√1−12μ2=√2μ2−12μ2...........(3)fromequation(2)and(3)1μ=√2μ2−12μ2Squaring both sides then solving we get =√32

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