A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12cm from P. At what point does the beam converge if the lens is a convex lens of focal length 20cm?

1. 7.5 cm away from the lens on the left side.
2. 7.5 cm away from the lens on the right side.
3. 6.5 cm away from the lens on the left side.
4. 6.5 cm away from the lens on the right side.

An object of size 3.0 cm is placed 14 cm in front of a concave lens of focal length 21 cm.  the image produced by the lens is:

1. inverted and virtual.
2. erect and real. 
3. erect and virtual. 
4. inverted and real.

What is the focal length of a convex lens of focal length \(30\) cm in contact with a concave lens of focal length \(20\) cm?
(Ignore the thickness of the lenses.)
1. \(-45~\mathrm{cm}\)
2. \(-55~\mathrm{cm}\)
3. \(-50~\mathrm{cm}\)
4. \(-60~\mathrm{cm}\)

The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall 3 m away by means of a large convex lens. What is the maximum possible focal length of the lens required for the purpose?

1. 0.60 cm
2. 0.01 m
3. 0.75 m
4. 0.65 m

A screen is placed \(90~\text{cm}\) from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by \(20~\text{cm}\). The focal length of the lens is:
1. \(18.81~\text{cm}\)
2. \(20.04~\text{cm}\)
3. \(13.01~\text{cm}\)
4. \(21.39~\text{cm}\)

A man with a normal near point (\(25~\text{cm}\)) reads a book with small print, using a magnifying glass: a thin convex lens of focal length \(5~\text{cm}\). What is the closest distance at which he should keep the lens from the page so that he can read the book when viewing through the magnifying glass?
1. \(3.5~\text{cm}\)
2. \(4.2~\text{cm}\)
3. \(4.9~\text{cm}\)
4. \(5.0~\text{cm}\)

A card sheet divided into squares each of size \(1~\text{mm}^{2}\) is being viewed at a distance of \(9~\text{cm}\) through a magnifying glass (a converging lens of focal length \(10~\text{cm}\)) held close to the eye. What is the magnification produced by the lens? 
1. 11
2. 9
3. 10
4. 12
 

A card sheet divided into squares each of size \(1~\text{mm}^2\) is being viewed at a distance of \(9~\text{cm}\) through a magnifying glass (a converging lens of focal length \(10~\text{cm}\)) held close to the eye. The angular magnification of the lens is:
1. \(3.34\)
2. \(1.55\)
3. \(3.03\)
4. \(2.78\)

Figure shows a biconvex lens (of refractive index 1.50) in contact with a liquid layer on top of a plane mirror. A small needle with its tip on the principal axis is moved along the axis until its inverted image is found at the position of the needle. The distance of the needle from the lens is measured to be 45.0 cm. The liquid is removed and the experiment is repeated. The new distance is measured to be 30.0 cm. What is the refractive index of the liquid?

1. 1.65
2. 1.51
3. 1.23
4. 1.33