A fish at a depth y inside the water is seeing a bird. The bird is at a height x above the water level. If the refractive index of water is $\mathrm{\mu }$, then the apparent distance of bird as seen by the fish is:

1.  x + $\mathrm{\mu }$y

2.  y + $\mathrm{\mu }$x

3.  x + $\frac{\mathrm{y}}{\mathrm{\mu }}$

4.  y + $\frac{\mathrm{x}}{\mathrm{\mu }}$

The magnification of a compound microscope for the final image at the least distance of distinct vision is \(90\). The magnification of the objective lens is \(15\). The value of the focal length of the eyepiece will be: 
1. \(5\) cm
2. \(6\) cm
3. \(1\over6\) cm
4. \(12\) cm

When an object is placed at 10 cm and 30 cm from a convex lens, images obtained are of the same magnitude of magnification. The focal length of the lens may be:

One of the refracting surfaces of a prism is silvered. A ray is incident at an angle \(60^{\circ}\), such that it retraces its path. The angle of the prism is: ($\mu$ = $\sqrt{3}$)

1. \(30^{\circ}\)$$

2. \(45^{\circ}\)$$

3. \(60^{\circ}\)$$

4. \(75^{\circ}\)$$

A concave lens forms the image of an object such that the distance between the object and image is 10 cm. If magnification of the image is $\frac{1}{4}$, the focal length of the lens is:

1.  $-\frac{20}{3}$ cm

2.  $\frac{20}{3}$ cm

3.  $\frac{40}{9}$ cm

4.  $-\frac{40}{9}$ cm

A ray of light incident on a prism of angle A and refractive index $\mu$ will not emerge out of the prism for any angle of incidence, if:

1.  $\mu$ > $\sin \frac{A}{2}$

2.  $\mu$ > cosA

3.  $\mu$ <$$ $\frac{1}{\sin A}$

4.  $\mu$ > $$ $\frac{1}{\sin {\displaystyle \frac{A}{2}}}$

In normal adjustment, the angular magnification of an astronomical telescope is 39. If length of the tube is 2 m, then focal length of the objective and eyepiece are respectively:

1. 195 cm, 5 cm

2. 190 cm, 10 cm

3. 20 cm, 180 cm

4. 10 cm, 190 cm

A ray of light is incident on an equilateral prism at an angle of incidence i such that it is incident normally on other refracting faces. Find 'i'. [Take $\mu$_glass =2]

1. \(30^{\circ}\)$$

2. \(45^{\circ}\)$$

3. \(60^{\circ}\)$$

4. Not possible

The ratio of the velocity of light in a medium to the velocity of light in a vacuum is \(\frac{4}{5}\). If the ray of light is emerging from this medium into the air, then the critical angle for this interface of medium and air will be:

If a light ray is incident normally on face AB of a prism, then for no emergent ray from second face AC:
[$\mu$$\to$refractive index of glass of prism]