A prism of refractive index 2 has a refracting angle of 60^ . At what angle a ray must be incident on it so that it suffers a minimum deviation.

Correct answer: A. 45^ The relation for refractive index of prism is μ=( i)/( r) (1) The condition for minimum deviation is r=(A)/(2)= 60^ 2 =30^ Putting the given value of μ= 2 and r=30^ in eq (1), we get aligned 2 & = i 30^ So, i & = 2 × (1)/(2)= 1 2 i & = 45^ i & =45^ aligned

JIPMER 2005

Exam: JIPMER
Year: 2005
Subject: Physics
Chapter: Ray Optics

JIPMER 2005 · Physics · Ray Optics

A prism of refractive index 2 has a refracting angle of 60^ . At...

A prism of refractive index

\sqrt{2}

has a refracting angle of

60^{\circ}

. At what angle a ray must be incident on it so that it suffers a minimum deviation.

Options

A $45^{\circ}$
B $60^{\circ}$
C $90^{\circ}$
D $180^{\circ}$

Correct answer

A. $45^{\circ}$

Step-by-step solution

The relation for refractive index of prism is

\mu=\frac{\sin i}{\sin r} \ldots(1)

The condition for minimum deviation is

r=\frac{A}{2}=\frac{60^{\circ}}{2}=30^{\circ}

Putting the given value of

\mu=\sqrt{2} and r=30^{\circ}

in eq (1), we get

\begin{aligned} \sqrt{2} & =\frac{\sin i}{\sin 30^{\circ}} \\ \text{ So, } \quad \sin i & =\sqrt{2} \times \frac{1}{2}=\frac{1}{\sqrt{2}} \\ \sin i & =\sin 45^{\circ} \\ i & =45^{\circ}\end{aligned}

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