Apparent Depth

Q.

How much water should be filled in a container 21 cm in height, so that it appears half filled when viewed from the top of the container (given that ${}_a{\mu }_{\omega }=\frac{4}{3}$)

1. 15.0 cm

2. 8.0 cm

3. 12.0 cm

4. 10.5 cm

Q. The correct relation between the radius of curvature ($\text{R}$), distance of object from the mirror ($\text{u}$), and distance of image formed ($\text{v}$) from the mirror is

1. $\frac{1}{\text{R}}=\frac{1}{\text{v}}+\frac{1}{\text{u}}$
2. $\text{R}=\frac{2}{\text{u + v}}$
3. $\text{R}=\frac{2\left(\text{u + v}\right)}{\text{uv}}$
4. $\text{R}=\frac{2\text{uv}}{\text{u + v}}$

Q.

Apparent depth for point object $x$ in all three cases are $H_1,H_2\&H_3$ respectively when seen from below given $H=30cm$, $n=1.5$ & $R=3m$, then

1. $0.8<H_2–H_1<0.9$

2. $H_2>H_1$

3. $H_2>H_3$

4. $H_3>H_1$

Q. Photographs of the ground are taken from an aircraft flying at an altitude of 2000 m by a camera with a lens of focal length 50 cm. The size of the film in the camera is $18cm\times 18cm.$ The area of the ground that can be photographed by the camera is:

1. $720m\times 720m$
2. $720cm\times 720cm$
3. $360cm\times 360cm$
4. None of these

Q.

A plane mirror is placed at the bottom of the tank containing a liquid of refractive index μ. P is a small object at a height h above the mirror. An observer O-vertically above P outside the liquid see P and its image in the mirror. The apparent distance between these two will be

1. $\frac{2h}{\mu }$

2. $2\mu h$

3. $\frac{2h}{\mu -1}$

4. $h(1+\frac{1}{\mu })$