A rectangular block is composed of three different glass prisms (with refractive indices \mu_1, \mu_2 and \mu_3) as shown in the figure below. A ray of light incident normal to the left face emerges normal to the right face. Then the refractive indices are related by

Correct Answer is : µ12+µ32=2µ22

\mu_1^ 2 + \mu_2 ^2 = 2\mu_3^ 2

\mu_1^ 2 + \mu_3 ^2 = 2\mu_2^ 2

\mu_2^ 2 + \mu_3 ^2 = 2\mu_1^ 2

KVPY SA Exam 2016 Question Paper

Question : 67 of 80

Marks: +1, -0

A rectangular block is composed of three different glass prisms (with refractive indices

µ_1, µ_2

and

µ_3

) as shown in the figure below. A ray of light incident normal to the left face emerges normal to the right face. Then the refractive indices are related by

$µ_1^ 2 + µ_2 ^2 = 2µ_3^ 2$
$µ_1 ^2 + µ_2^ 2 = µ_3^ 2$
$µ_1^ 2 + µ_3 ^2 = 2µ_2^ 2$
$µ_2^ 2 + µ_3 ^2 = 2µ_1^ 2$

Validate

Solution:

for surface AB:

µ_1 \sin 45º = µ_2 \sin θ_1

… (1)
for surface AC:

µ_2 \sin (ω - θ_1) = µ_3 \sin 45

µ_3 \sin 45º = µ_2 \cos θ_1

… (2) (ω = 90º)
Squaring and adding equation (1) & (2)

µ_1^2/2+µ_3^2/2=µ_2^2

⇒µ_1^2+µ_3^2=2µ_2^2

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