Question

For a glass prism(μ=√3) the angle of minimum deviation is equal to the angle of the prism. Calculate the angle of the prism.

Answer 1

From the formula μ =sin[(A+D) /2]/sin A/2
where,μ= refractive index of the prism.
A= angle of prism
D=angle of minimum deviation.
Given, A=D; μ=√3
So, putting in formula, we get, A=60°.

Answer 2

Answer:

The angle of the prism is 60°.

Explanation:

The refractive index of a prism in terms of angle of deviation and prism angle is calculated as,

$\mu=\frac{sin(\frac{A+\delta}{2}) }{sin\frac{A}{2} }$        (1)

Where,

μ=refractive index of a prism

A=angle of a prism

δ=angle of minimum deviation

From the question we have,

μ=√3

A=δ (the angle of minimum deviation is equal to the angle of the prism)

By placing the required values in equation (1) we get;

$\sqrt{3} =\frac{sin(\frac{A+A}{2}) }{sin\frac{A}{2} }$

$\sqrt{3} =\frac{sin A }{sin\frac{A}{2} }$

$\sqrt{3} =\frac{2sin \frac{A}{2}cos\frac{A}{2}}{sin\frac{A}{2} }$

$cos\frac{A}{2}=\frac{\sqrt{3} }{2}$

$cos\frac{A}{2}=cos 30\textdegree$

$A=2\times 30\textdegree$

$A=60\textdegree$

Hence, the angle of the prism is 60°.

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