Two identical thin plano-convex glass lenses (refractive index = 1.5) each having radius of curvature of 20 cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of refractive index 1.7. The focal length of the combination is:
1. -20 cm
2. -25 cm
3. -50 cm
4. 50 cm

If the focal length of the objective lens is increased then magnifying power of:

1. microscope will increase but that of the telescope
    decrease.

2. microscope and telescope both will increase.

3. microscope and telescope both will decrease.

4. microscope will decrease but that of the telescope
    will increase.

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. $\frac{1}{2}$cosA

4. tanA

For a normal eye, the cornea of the eye provides a converging power of 40 D and the least converging power of the eye lens behind the cornea is 20 D. Using this information, the distance between the retina and the cornea-eye lens can be estimated to be:
1. 2.5 cm
2. 1.67 cm
3. 1.5 cm
4. 5 cm

When a biconvex lens of glass having a refractive index of 1.47 is dipped in a liquid, it acts as a plane sheet of glass. The liquid must have a refractive index:

1. equal to that of glass.

2. less than one.

3. greater than that of glass.

4. less than that of glass.

A ray of light is incident at an angle of incidence, i, on one face of a prism of angle A (assumed to be small) and emerges normally from the opposite face. If the refractive index of the prism is $\mu$, the angle of incidence i, is nearly equal to

1. $\mu$A

2. $\frac{\mu A}{2}$

3. $A/\mu$

4. $A/2\mu$

A concave mirror of the focal length $f_1$ is placed at a distance of d from a convex lens of focal length $f_2$. A beam of light coming from infinity and falling on this convex lens-concave mirror combination returns to infinity. The distance d must be equal to:

1. $f_1+f_2$

2. $-f_1+f_2$

3. $2f_1+f_2$

4. $-2f_1+f_2$

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

1. 10 cm, 10 cm

2. 15 cm, 5 cm

3. 18 cm, 2 cm

4. 11 cm, 9 cm