The image formed by a concave mirror:

1.	is always real
2.	is always virtual
3.	is certainly real if the object is virtual
4.	is certainly virtual if the object is real

The figure shows three transparent media of refractive indices \(\mu_1,~\mu_2\) and \(\mu_3\). A point object \(O\) is placed in the medium \(\mu_2\). If the entire medium on the right of the spherical surface has refractive index \(\mu_1\), the image forms at \(O'.\) If this entire medium has refractive index \(\mu_3\), the image forms at \(O''.\) In the situation shown,

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