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:

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:

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 would be:
1. \(2 D\)
2. \(3 D\)
3. \(4 D\)
4. \(5D\)

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:
1. becomes undefined.
2. remains unchanged.
3. increases.
4. decreases.

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:

A point object \(O\) is placed on the principal axis of a convex lens of focal length \(f = 20~\text{cm}\) at a distance of \(40~\text{cm}\) to the left of it. The diameter of the lens is \(10~\text{cm}.\) An eye is placed \(60~\text{cm}\) to the right of the lens and a distance \(h\) below the principal axis. The maximum value of \(h\) to see the image is:
(assume paraxial approximation to be valid here)
1. Zero
2. \(2.5~\text{cm}\)
3. \(5~\text{cm}\)
4. \(10~\text{cm}\)