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

A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that its end closer to the pole is 20 cm away from the mirror. The length of the image is:

A ray of light traveling in a transparent medium of refractive index $\mu$ falls, on a surface separating the medium from the air at an angle of incidence of 45$°$.For which of the following value of $\mu$ the ray can undergo total internal reflection?

(1) $\mu =1.33$                             

(2) $\mu =1.40$

(3) $\mu =1.50$                             

(4) $\mu =1.25$

The speed of light in media ${\mathrm{M}}_1$ and ${\mathrm{M}}_2$ is $1.5\times {10}^8 \mathrm{m}/\mathrm{s}$ and $2.0\times {10}^8 \mathrm{m}/\mathrm{s}$ respectively. A ray of light enters from medium ${\mathrm{M}}_1$ to ${\mathrm{M}}_2$ at an incidence angle i. If the ray suffers total internal reflection, the value of i is

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

(2) equal to or less than ${\sin }^{-1}\left(\frac{3}{5}\right)$

(3) equal to or greater than ${\sin }^{-1}\left(\frac{3}{4}\right)$

(4) less than ${\sin }^{-1}\left(\frac{2}{3}\right)$