KVPY SA Exam 2014 Question Paper

Question : 69 of 80

Marks: +1, -0

A ray of light incident parallel to the base PQ of anisosceles right-angled triangular prism PQR suffers twosuccessive total internal reflections at the faces PQ and ORbefore emerging reversed in direction as shown.

If the refractive index of the material of the prism is p, then

$µ > √5$
$√3 < µ < √5$
$√2 <µ <√3$
$µ <√2$

Validate

Solution:

45 + r > θ_c

……. (1)

45 - r > θ_c

……. (2)

90º > 2θ_c

45º > θ_c

……. (3)

\sin 45º > \sin θ _c

1/√2>1/µ

µ>√2

taking equation 2 only

45- θ_c > r , \sin( 45 - θ_c) > \sin r

1/ √2\ cos θ_c -1/√2\sin θ_c >{\sin 45}/μ

{√µ^2-1}/µ-1/µ>1/µ,√µ^2-1>2,

[µ>√5]

∴ Ans. is

μ > √5

as this is common solution

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