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:
          

1.	\(20~\text{cm}\)	2.	\(30~\text{cm}\)
3.	\(40~\text{cm}\)	4.	\(50~\text{cm}\)

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

Two identical glass $\left({\mu }_g=3/2\right)$ equi-convex lenses of focal length $f$ each are kept in contact. The space between the two lenses is filled with water $\left({\mu }_w=4/3\right)$. The focal length of the combination is

1.  $f/3$             
2. $f$
3. $\frac{4f}{3}$               
4. $\frac{3f}{4}$

An air bubble in a glass slab with refractive index 1.5 (near normal incidence) is 5 cm deep when viewed from one surface and  3 cm deep when viewed from the opposite face. The thickness (in cm) of the slab is

1. 8           

2. 10

3. 12         

4. 16

A person can see clearly objects only when they lie between 50 cm and 400 cm from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use will be-

1. convex, +2.25 diopter

2. concave, - 0.25 diopter

3. concave, - 0.2 diopter

4. convex, + 0.15 diopter

Match the corresponding entries of Column 1 with Column 2. [Where m is the magnification produced by the mirror]

Column 1                         Column 2 
A. m=-2                     a. Convex mirror   
B. m=-1/2                  b. Concave mirror
C. m=+2                    c. Real image
D. m=+1/2                 d. Virtual Image

1. A->a and c;B->a and d; C->a and b; D->c and d

2. A->a and d; B->b and c; C->b and d; D-> b and c

3. A->c and d; B->b and d;C->b and c;D->a and d

4. A->b and c; B->b and c; C->b and d; D->a and d

The angle of a prism is A. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index μ of the prism is

1. 2sinA
 

2. 2cosA
 

3. 1/2cosA
 

4. tanA