The linear magnification and angular magnification in the microscope have similar magnitude when the image is at a distance of:
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

A light incident normally on a plane mirror attached to a galvanometer coil retraces backward as shown in the figure. A current in the coil produces a deflection of \(3.5^\circ\) of the mirror. What is the displacement of the reflected spot of light on a screen placed \(1.5~\text m\) away?
(given \(\tan (7)^\circ =0.1228\))

1. \(15.0~\text{cm}\)
2. \(18.4~\text{cm}\)
3. \(21.2~\text{cm}\)
4. \(12.5~\text{cm}\)

A Cassegrain telescope uses two mirrors as shown in the figure. Such a telescope is built with the mirrors 20 mm apart. If the radius of curvature of the large mirror is 220 mm and the small mirror is 140 mm, where will the final image of an object at infinity be?

1. 315 mm away from the secondary mirror.
2. 315 mm towards the secondary mirror.
3. 313 mm away from the secondary mirror.
4. 313 mm towards the secondary mirror.

An angular magnification (magnifying power) of \(30\mathrm{X}\) is desired using an objective of focal length \(1.25~\text{cm}\) and an eyepiece of focal length \(5~\text{cm}\). The separation between the objective lens and the eyepiece should be:
1. \(11.67~\text{cm}\)
2. \(10.23~\text{cm}\)
3. \(12.21~\text{cm}\)
4. \(13.13~\text{cm}\)

Digital movie projectors work on the principle of:

(1) Reflection from micromirrors

(2) Refraction from thin lenses

(3) Dispersion from thin prisms

(4) Total internal reflection from optical fibres

Day and night settings for rearview mirrors use:

(1) Thin mirrors

(2) Thick wedge-shaped mirrors

(3) Convex mirrors

(4) Concave mirrors

When a beam of light is incident on a plane mirror, it is found that a real image is formed. The incident beam must be:

(1) Converging

(2) Diverging

(3) Parallel

(4) Formation of the real image by a plane mirror is impossible

An object is placed symmetrically between two plane mirrors inclined at an angle of 72^o, then the total number of images observed is:

(1) 5

(2) 4

(3) 2

(4) Infinite

A person 1.6 m tall is standing at the centre between two walls three metres high. What should be the minimum size of a plane mirror fixed on the wall in front of him if he is to see the full height of the wall behind him?

(1) 0.8 m

(2) 1 m

(3) 1.5 m

(4) 2.3 m