Four modifications are suggested in the lens formula to include the effect of the thickness t of the lens. Which one is likely to be correct?

1. \(\frac{1}{v}-\frac{1}{u}=\frac{t}{u f}\)

2. \(\frac{t}{v^{2}}-\frac{1}{u}=\frac{1}{f}\)

3. \(\frac{1}{v-t}-\frac{1}{u+t}=\frac{1}{f}\)

4. \(\frac{1}{v}-\frac{1}{u}+\frac{t}{u v}=\frac{t}{f}\)

A point source of light is placed at a distance of 2 f from a converging lens of focal length f. The intensity on the other side of the lens is maximum at a distance

1. f

2. between f and 2 f

3. 2 f

3.  more than 2 f

A parallel beam of light is incident on a converging lens parallel to its principal axis. As one moves away from the lens on the other side on its principal axis, the intensity of light

1. remains constant

2. continuously increases

3. continuously decreases

4. first increases then decreases

A symmetric double convex lens is cut in two equal parts by a plane containing the principal axis. If the power of the original lens was \(4~\text{D}\), the power of a divided lens will be:
1. \(2~\text{D}\) 
2. \(3~\text{D}\) 
3. \(4~\text{D}\) 
4. \(5~\text{D}\) 

Two concave lenses \(L_1\) and \(L_2\) are kept in contact with each other. If the space between the two lenses is filled with a material of smaller refractive index, the magnitude of the focal length of the combination:

 A point object O is placed on the principal axis of a convex lens of focal length f = 20 cm at a distance of 40 cm to the left of it. The diameter of the lens is 10 cm. An eye is placed 60 cm to right of the lens and a distance h below the principal axis. The maximum value of h to see the image is

1. 0

2. 2.5 cm

3. 5 cm

4. 10 cm

The rays of different colours fail to converge at a point after going through a converging lens. This defect is called:
1. spherical aberration
2. distortion
3. coma
4. chromatic aberration

A convex lens forms a real image of a point object placed on its principal axis. If the upper half of the lens is painted black,

Choose the correct option:

A screen is placed a distance 40 cm away from an illuminated object. A converging lens is placed between the source and the screen and it is attempted to form the image of the source on the screen. If no position could be found, the focal length of the lens

1. must be less than 10 cm

2. must be greater than 20 cm

3. must not be greater than 20 cm

4. must not be less than 10 cm

The focal length of a converging lens are f_v and f_r for violet and red light respectively.

1. f_v > f_r

2. f_v = f_r

3. f_v < f_r

4. Any of the three is possible depending on the value of the average refractive index \(\mu\)