In an astronomical telescope in normal adjustment, a straight line of length \(L\) is drawn on inside part of the objective lens. The eye-piece forms a real image of this line. The length of this image is \(I.\) The magnification of the telescope is:
1. $\frac{L}{I}+1$

2. $\frac{L}{I}-1$

3. $\frac{L+1}{I-1}$

4. $\frac{L}{I}$

A beam of light consisting of red, green, and blue colours is incident on a right-angled prism. The refractive index of the material of the prism for the red, green, and blue wavelengths is 1.39, 1.44, and 1.47 respectively. 
  
The prism will:

1. separate the blue colour part from the red and
    green colour

2. separate all the three colours from one another

3. not separate the three colours at all 

4. separate the red color part from the green and
    blue colours

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. $A/2\mu$