The refractive index of the material of a prism is $\sqrt{\mathrm{2 }}$and the angle of the prism is \(30^\circ.\) One of the two refracting surfaces of the prism is made a mirror inwards with a silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if the angle of incidence on the prism is:

A thin prism having refracting angle \(10^\circ\) is made of glass of a refractive index \(1.42\). This prism is combined with another thin prism of glass with a refractive index \(1.7\). This combination produces dispersion without deviation. The refracting angle of the second prism should be:
1. \(6^{\circ}\)
2. \(8^{\circ}\)
3. \(10^{\circ}\)
4. \(4^{\circ}\)

The angle of incidence for a ray of light at a refracting surface of a prism is 45°. The angle of prism is 60°. If the ray suffers minimum deviation through the prism, the angle of deviation and refracting index of the material of the prism respectively are

(a)30°,$\sqrt{2}$

(b)45°,$\sqrt{2}$

(c)30°,$\frac{1}{\sqrt{2}}$

(d)45°,$\frac{1}{\sqrt{2}}$

The angle of incidence for a ray of light at a refracting surface of a prism is \(45^{\circ}\). The angle of the prism is \(60^{\circ}\). If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are: