Question

If the angle of minimum deviation produced by an equilateral prism is 30${}^{\circ }$, the refractive index of material of prism is :

• A. $\sqrt{2}$
• B. $1.5$
• C. $1.6$
• D. $\sqrt{3}$

Answer 1

Answer: (A)

The correct option is A $\sqrt{2}$

According to the question angle of minimum deviation ${\delta }_m={30}^0$

Given that the prism is equilateral

So the angle of prism $A={60}^0$

We know the refractive index is given as

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

Putting all the values

$\mu =\frac{sin\frac{60+30}{2}}{sin\frac{A}{2}}$

After solving we get

$\mu =\sqrt{2}$

Hence the refractive index is $\mu =\sqrt{2}$

δm=30⋅\delta_m=30^{\cdot

μ=sinA+δm2sinA2\mu =\dfrac{sin\dfrac{A + \delta_m}{2}}{sin\dfrac{A}{2}}