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 double convex lens has two surfaces of equal radii \(R\) and refractive index \(m=1.5.\) We have:
1. \(f=R/2\)
2. \(f=R \)
3. \(f=-R\)
4. \(f=2R\)

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 perpendicular to the principal axis. If the power of the original lens was 4 D, the power of a cut-lens will be

1. 2 D

2. 3 D

3. 4 D

4. 5 D

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 thin lens is made with a material having refractive index \(\mu=1.5\). Both sides are convex. It is dipped in water (\(\mu=1.33\)). It will behave like:
1. a convergent lens
2. a divergent lens
3. a rectangular slab
4. a prism

A convex lens is made of a material having refractive index \(1.2.\) Both the surfaces of the lens are convex. If it is dipped into water (\(\mu=1.33\) ), it will behave like:
1. a convergent lens
2. a divergent lens
3. a rectangular slab
4. a prism

 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