Why Spherical over Parabolic

Q. A ray of light is incident at an angle of ${45}_o$ on a square slab of a transparent material. What should be the refractive index of the material of the slab so that total internal reflection occurs at the vertical face AB.

(IIT-JEE 2005)

1. $\sqrt{2}$
2. $\sqrt{\frac{3}{2}}$
3. 1.5
4. $\sqrt{\frac{5}{3}}$

Q. A fish looking up through water sees the outside world contained in a circular horizon. If the refractive index of water is $\frac{4}{3}$ and the fish is 12 cm below the surface, the radius of this circle (in cm) is

1. $4\sqrt{5}$
2. $36\sqrt{5}$
3. $36\sqrt{7}$
4. $\frac{36}{\sqrt{7}}$

Q. If the side towards the centre of curvature is shining, then the type of mirror is:

1. Concave
2. Convex
3. Either concave or convex
4. Neither concave nor convex

Q. A glass prism of refractive index 1.5 is immersed in water (refractive index $\frac{4}{3}$). A light beam normally on the face AB is totally reflected to reach on the face BC if

1. $sin\theta \ge \frac{8}{9}$
2. $\frac{3}{2}<sin\theta \ge <\frac{8}{9}$
3. $sin\theta \le \frac{3}{2}$
4. $sin\theta \le \frac{8}{9}$

Q. Angle of prism is A and its one surface is silvered. Light rays falling at an angle of incidence 2A on first surface return back through the same path after suffering reflection at second silvered surface. Refractive index of material is

1. 2 sin A
2. 2 cos A
3. $cos\frac{A}{2}$
4. tan A