One face of a prism of apex angle 30$°$ is silvered and a ray of light is incident on the first face at an angle i such that it retraces its entire path after reflection from the silvered face. If the refractive index of prism material is 2, then the value of i must be -

1.  45$°$

2.  60$°$

3.  30$°$

4.  90$°$

A ray of light incident on an equilateral prism at grazing incidence emerges from the prism at grazing emergence. The Refractive index of the prism is:

1. 1.5

2. 1.8

3. 1.33

4. 2

The refractive index of the material of the prism for violet colour is 1.69 and that for red is 1.65. If the refractive index for mean colour is 1.66, the dispersive power of the material of the prism

1.  0.66

2.  0.06

3.  0.65

4.  0.69

Two identical equiconvex thin lenses each of focal lengths 20 cm, made of material of refractive index 1.5 are placed coaxially in contact as shown. Now, the space between them is filled with a liquid with a refractive index of 1.5. The equivalent power of this arrangement will be:

In the situation shown, the incident monochromatic ray retraces its path after its incidence on the silvered surface. The speed of light inside the prism will be

1.  $3 \mathrm{x} {10}^8 {\mathrm{ms}}^{-1}$

2.  $2 \mathrm{x} {10}^8 {\mathrm{ms}}^{-1}$

3.  $1.41 \mathrm{x} {10}^8 {\mathrm{ms}}^{-1}$

4.  $1.73 \mathrm{x} {10}^8 {\mathrm{ms}}^{-1}$

When a ray is refracted from one medium to another, the wavelength changes from 6000$\stackrel{0}{\mathrm{A}}$ to 4000$\stackrel{0}{\mathrm{A}}$. The critical  angle for the interface will be:

1.  ${\cos }^{-1} \left(\frac{2}{3}\right)$

2.  ${\sin }^{-1}\left(\frac{2}{\sqrt{3}}\right)$

3.  ${\sin }^{-1}\left(\frac{2}{3}\right)$

4.  ${\cos }^{-1}\left(\frac{2}{\sqrt{3}}\right)$

A ray of light falls on a transparent sphere as shown in the figure. If the final ray emerges from the sphere parallel to the horizontal diameter, then calculate the refractive index of the sphere. Consider that the sphere is kept in the air.
                                   
1.  $\sqrt{2}$ $$ 

2.  $\sqrt{3}$ $$

3.  $\sqrt{3/2}$ $$

4.  $\sqrt{4/3}$

Two plane mirrors, \(A\) and \(B\) are aligned parallel to each other, as shown in the figure. A light ray is incident at an angle of \(30^\circ\) at a point just inside one end of \(A\). The plane of incidence coincides with the plane of the figure. The maximum number of times the ray undergoes reflections (excluding the first one) before it emerges out is:
   
1. \(28\)                     
2. \(30\)
3. \(32\)         
4. \(34\)

A square of side 3 cm  is placed at a distance of 25 cm from a concave mirror of focal length 10 cm. The centre of the square is at the axis of the mirror and the plane is normal to the axis. The area enclosed by the image of the square is:

One face of a rectangular glass plate 6 cm thick is silvered. An object held 8 cm in front of the first face, forms an image 10 cm behind the silvered face. The refractive index of the glass is [Consider that light ray returns back in the first medium]

(1) 0.4                     

(2) 0.8

(3) 1.5                     

(4) 1.6