What is the focal length of a convex lens of focal length \(30~\text{cm}\) in contact with a concave lens of focal length \(20~\text{cm}\)?
(Ignore the thickness of the lenses.)

1.	\(-45~\text{cm}\)	2.	\(-55~\text{cm}\)
3.	\(-50~\text{cm}\)	4.	\(-60~\text{cm}\)

A compound microscope consists of an objective lens of focal length \(2.0~\text{cm}\) and an eyepiece of focal length \(6.25~\text{cm}\) separated by a distance of \(15~\text{cm}.\) How far from the objective should an object be placed in order to obtain the final image at the least distance of distinct vision \((25~\text{cm})?\)
1. \(2.5~\text{cm}\)
2. \(0.5~\text{cm}\)
3. \(1.5~\text{cm}\)
4. \(5.0~\text{cm}\)

A person with a normal near point \((25~\text{cm})\) using a compound microscope with an objective of focal length \(8.0~\text{mm}\)  and an eyepiece of focal length \(2.5~\text{cm}\) can bring an object placed at \(9.0~\text{mm}\) from the objective in sharp focus. What is the separation between the two lenses?
1. \(7.20~\text{cm}\)
2. \(9.47~\text{cm}\)
3. \(2.50~\text{cm}\)
4. \(2.27~\text{cm}\)

A small telescope has an objective lens of a focal length \(144~\text{cm}\)  and an eyepiece of focal length \(6.0~\text{cm}.\) What is the magnifying power of the telescope?

A giant refracting telescope at an observatory has an objective lens of focal length \(15\) m. If an eyepiece of focal length \(1.0\) cm is used, what is the angular magnification of the telescope?

A small pin fixed on a table top is viewed from above from a distance of \(50~\text{cm}\). By what distance would the pin appear to be raised if it is viewed from the same point through a \(15~\text{cm}\) thick glass slab held parallel to the table? (The refractive index of glass is \(1.5\))

A cross-section of a ‘light pipe’ made of a glass fiber of refractive index \(1.68.\) The outer covering of the pipe is made of a material with a refractive index of \(1.44.\) What is the range of the angles of the incident rays with the axis of the pipe for which total reflections inside the pipe take place, as shown in the figure?

     
1. \(0^\circ<i<45^\circ\)
2. \(0^\circ<i<60^\circ\)
3. \(45^\circ<i<75^\circ\)
4. \(45^\circ<i<90^\circ\)

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. \(21.39~\text{cm}\)

At what angle should a ray of light be incident on the face of a prism of refracting angle \(60^{\circ}\) so that it just suffers total internal reflection at the other face?
(the refractive index of the material of the prism is \(1.524\))
1. \(29.75^\circ\)
2.\(19^\circ\)
3.\(17.23^\circ\)
4.\(19.57^\circ\)