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:

1.	\(4~\text{cm}^2 \)	2.	\(6~\text{cm}^2 \)
3.	\(16~\text{cm}^2 \)	4.	\(36~\text{cm}^2 \)

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

The image of point P when viewed from the top of the slabs will be

1.  2.0 cm above P

2. 1.5 cm above P

3.  2.0 cm below P

4.  1 cm above P

2. \(R\)
3. \(\frac{3}{2}R\)
4. \(R^2\)

A rectangular glass slab ABCD, of refractive index $n_1$, is immersed in water of the refractive index $n_2\left(n_1>n_2\right)$. A ray of light is incident at the surface AB of the slab as shown. The maximum value of the angle of incidence ${\alpha }_{max}$, such that the ray comes out only from the other surface CD is given by

1.  ${\sin }^{-1}\left[\frac{n_1}{n_2}\cos \left({\sin }^{-1}\frac{n_2}{n_1}\right)\right]$           

2.  ${\sin }^{-1}\left[n_1\cos \left({\sin }^{-1}\frac{1}{n_2}\right)\right]$

3.  ${\sin }^{-1}\left(\frac{n_1}{n_2}\right)$                           

4.  ${\sin }^{-1}\left(\frac{n_2}{n_1}\right)$           

The slab of a refractive index material equal to \(2\) shown in the figure has a curved surface \(APB\) of a radius of curvature of \(10~\text{cm}\) and a plane surface \(CD.\) On the left of \(APB\) is air and on the right of \(CD\) is water with refractive indices as given in the figure. An object \(O\) is placed at a distance of \(15~\text{cm}\) from the pole \(P\) as shown. The distance of the final image of \(O\) from \(P\) as viewed from the left is:
          

The focal length of the objective lens and the eye lens is 4 mm and 25 mm respectively in a compound microscope. The  distance between objective and eyepiece lens is 16 cm. Find its magnifying power for relaxed eye position-

1.  32.75                                 

2.  327.5 

3.  0.3275                               

4. None of the above

An air bubble in a sphere having 4 cm diameter that appears 1 cm from the surface nearest to the eye when looked along diameter. If${}_a\mu _g$ = 1.5, the distance of bubble from the refracting surface is

1.  1.2 cm                   

2.  3.2 cm

3.  2.8 cm           

4.  1.6 cm

Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of the surfaces of the lenses are as given in the diagrams          

1.		2.
3.		4.

A plano-convex lens when silvered in the plane side behaves like a concave mirror of

focal length 30 cm. However, when silvered on the convex side it behaves like a concave

mirror of focal length 10 cm. Then the refractive index of its material will be 

1. 3.0                               

2. 2.0

3. 2.5                               

4. 1.5