A diverging lens with the magnitude of focal length \(25~\text{cm}\) is placed at a distance of \(15~\text{cm}\) from a converging lens of magnitude of focal length \(20~\text{cm}\). A beam of parallel light falls on the diverging lens. The final image formed as:

An upright object is placed at a distance of \(40~\text{cm}\) in front of a convergent lens of focal length \(20~\text{cm}\). A convergent mirror of focal length \(10~\text{cm}\) is placed at a distance of \(60~\text{cm}\) on the other side of the lens. The position and size of the final image will be:

A convex lens (of focal length \(20\) cm) and a concave mirror, having their principal axes along the same lines, are kept \(80\) cm apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of \(30\) cm to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be:
1. \(20~\text{cm}\)
2. \(10~\text{cm}\)
3. \(25~\text{cm}\)
4. \(30~\text{cm}\)

A convex lens of focal length \(20~\text{cm}\) produces images of the same magnification \(2\) when an object is kept at two distance \(x_1\) and \(x_2\) (\(x_1>x_2\)) from the lens. The ratio of \(x_1\) and \(x_2\) is:
1. \(4:3\)
2. \(3:1\)
3. \(2:1\)
4. \(5:3\)

The graph shows how the magnification \(m\) produced by a thin lens varies with image distance \(v\). What is the focal length of the lens used?

     
1. \( \frac{b^2 c}{a} \)
2. \(\frac{b}{c} \)
3. \(\frac{b^2}{a c} \)
4. \(\frac{a}{c}\)

The distance between an object and a screen is \(100~\text{cm}\). A lens can produce real image of the object on the screen for two different positions between the screen and the object. The distance between these two positions is \(40~\text{cm}\). If the power of the lens is close to \(\left(\frac{N}{100}\right)D\) where \(N\) is an integer, the value of \(N\) is:
1. \(245\)
2. \(476\)
3. \(132\)
4. \(763\)

For a concave lens of focal length \(f\), the relation between object and image distance \(u\) and \(v\),
respectively, from its pole can best be represented by (\(u=v\) is the reference line):

1.		2.
3.		4.

A point like object is placed at a distance of \(1~\text{m}\) in front of a convex lens of focal length \(0.5~\text{m}\). A plane mirror is placed at a distance of \(2~\text{m}\) behind the lens. The position and nature of the final image formed by the system are: