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Question

A prism of refractive index √2 has refracting angle 600. In order that a ray suffers minimum deviation it should be incident at an angle:450900300none

A
300
B
none
C
450
D
900
Solution
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Given: A prism of refractive index √2 has refracting angle 60∘. To find the angle of incidence in order that a ray suffers minimum deviation Solution:As per the given criteria,refractive index of the prism, μ=√2Angle of the prism, A=60∘For minimum angle of deviation we have angle of incidence is equal to angle of emergence, i.e., i=eHence, i=A+δm2, where δm is the minimum deviation angle.We know,μ=sin(A+δm2)sinA2⟹√2=sinisin602⟹sini=√2×sin(30)⟹sini=√2×12Multiply and divide by √2, we getsini=1√2⟹i=45∘In order that a ray suffers minimum deviation it should be incident at an angle 45∘

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