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]

In a glass ($\mu$ = 1.5) sphere with a radius of 10 cm, there is an air bubble B at a distance of 5 cm from C. The distance of the bubble from the surface of the sphere (i.e., point A) as observed from point P in the air will be:

A lens forms an image of a point object placed at distance 20 cm from it. The image is formed just in front of the object at a distance 4 cm from the object (and towards the lens). The power of the lens is:

1.  $-$2.25 D

2.  1.75 D

3.  $-$1.25 D

4.  1.4 D

The distance between the object and its real image formed by a concave mirror is minimum when the distance of the object from the centre of curvature of the mirror is: [f $\to$ focal length of the mirror]
1.  Zero
2.  $\frac{\mathrm{f}}{2}$
3.  f
4.  2f