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

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

(a)  $f/3$             (b) $f$

(c) $\frac{4f}{3}$               (d) $\frac{3f}{4}$

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

A plane-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices μ₁ and μ₂ and R is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is:
1. R/2(μ_{1 +} μ₂)
2. R/2(μ_{1 -} μ₂)
3. R/(μ_{1 -} μ₂)
4. 2R/(μ₂ - μ₁)

The magnifying power of a telescope is 9. When it is adjusted for parallel rays the distance between the objective and eyepiece is 20cm. The focal length of lenses are 

(1) 10cm,10cm

(2) 15cm,5cm

(3) 18cm,2cm

(4) 11cm,9cm