A small candle, \(2.5\) cm in size is placed at \(27\) cm in front of a concave mirror of radius of curvature \(36\) cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image?

A \(4.5~\text{cm}\) needle is placed \(12~\text{cm}\) away from a convex mirror of focal length \(15~\text{cm}\). What is the magnification?
1. \(0.5\)
2. \(0.56\)
3. \(0.45\)
4. \(0.15\)

A small bulb is placed at the bottom of a tank containing water to a depth of 80 cm. What is the area of the surface of water through which light from the bulb can emerge out? The Refractive index of water is 1.33. (Consider the bulb to be a point source.)

1. 5.22 $m^{\mathrm{2 \; \; }}$
2. 1.33 $m^2$
3. 2.61 $m^2$
4 1.30 $m^2$

A prism is made of glass of unknown refractive index. A parallel beam of light is incident on the face of the prism. The angle of minimum deviation is measured to be \(40^\circ.\) What is the refractive index of the material of the prism?
(The refracting angle of the prism is \(60^\circ\))
1. \(1.43\)
2. \(1.33\)
3. \(1.50\)
4. \(1.53\)

Double-convex lenses are to be manufactured from a glass of refractive index \(1.55\) with both faces of the same radius of curvature. What is the radius of curvature required, if the focal length is to be \(20~\text{cm}\)?
1. \(20~\text{cm}\)
2. \(22~\text{cm}\)
3. \(24~\text{cm}\)
4. \(15~\text{cm}\)

A tank is filled with water to a height of \(12.5~\text{cm}.\) The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be \(9.4~\text{cm}.\) If water is replaced by a liquid of refractive index \(1.63\) up to the same height, by what distance would the microscope have to be moved to focus on the needle again?
1. \(1.73~\text{cm}\)
2. \(1.98~\text{cm}\)
3. \(1.01~\text{cm}\)
4. \(1.11~\text{cm}\)

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

 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. \(5.0~\text{cm}\)