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. \(15~\text{cm}\)

Monochromatic light of wavelength 589 nm is incident from the air on a water surface. What is the wavelength of reflected light? The refractive index of water is 1.33.

1. 500 nm
2. 545 nm
3. 485 nm
4. 589 nm

The refractive index of glass is 1.5. What is the speed of light in glass? 

1.\(2 \times 10^{8} m/s\)
2.\(3 \times 10^{8} m/s\)
3.\(1.5 \times 10^{8} m/s\)
4.\(2.2 \times 10^{8} m/s\)

Light of wavelength 5000 Å falls on a plane reflecting surface. For what angle of incidence is the reflected ray normal to the incident ray?
1. \(37^{\circ}\)
2. \(45^{\circ}\)
3. \(90^{\circ}\)
4. \(0^{\circ}\)

A tank is filled with water to a height of \(12.5\) cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be \(9.4\) 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. \(1.73\) cm
2. \(1.98\) cm
3. \(1.01\) cm
4. \(1.11\) 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.