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 of refractive index 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.\(19.57^\circ\)

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 man with 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 ratio of maximum and the minimum angular magnification (magnifying power) possible using the above simple microscope?
1. \(\frac65\)
2. \(\frac56\)
3. \(\frac32\)
4. \(\frac23\)

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. \(2.78\)

The linear magnification and angular magnification in the microscope have similar magnitude when the image is at a distance is:
1. \(35~\text{cm}\)
2. \(\infty\)
3. \(25~\text{cm}\)
4. none of these

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