The focal length of a convex lens is \(40~\text{cm}\) cm and the size of the inverted image formed is half of the object. The distance of the object is:

1.	\(60~\text{cm}\)	2.	\(120~\text{cm}\)
3.	\(30~\text{cm}\)	4.	\(180~\text{cm}\)

The condition of minimum deviation is achieved in an equilateral prism kept on the prism table of a spectrometer. If the angle of incidence is \(50^{\circ}\), the angle of deviation is:
1. \(25^{\circ}\)$$

2. \(40^{\circ}\)$$

3. \(50^{\circ}\)$$

4. \(60^{\circ}\)$$

A small air bubble is at the centre of a glass sphere of radius 10 cm and refractive index 1.5. The distance of the bubble from the surface, when viewed from outside the sphere, is

(1) 2.5 cm

(2) 5 cm

(3) 7.5 cm

(4) 10 cm

Focal lengths of objective and eyepiece of a compound microscope are 2 cm and 6.25 cm respectively. An object AB is placed at a distance of 2.5 cm from the objective which forms the image A'B' as shown in the figure. Maximum magnifying power in this case is

1.  10

2.  20

3.  5

4.  25

The refractive index of the material of prism is $\sqrt{2}$. The angle of prism A is equal to

(1) 30$°$

(2) 40$°$

(3) 60$°$

(4) 90$°$

An object is placed \(20~\text{cm}\) in front of a concave mirror of a radius of curvature \(10~\text{cm}.\) The position of the image from the pole of the mirror is:
1. \(7.67~\text{cm}\)
2. \(6.67~\text{cm}\)
3. \(8.67~\text{cm}\)
4. \(9.67~\text{cm}\)

A plane mirror is moving with velocity $4\hat{i}+5\hat{j}+8\hat{k}$. A point object in front of the mirror moves with a velocity  $3\widehat{i }+4\hat{j}+5\hat{k},$ here $\hat{k}$ is along the normal to the plane mirror and facing towards the object. The velocity of the image is

1. $-3\hat{i}-4\hat{j}+5\hat{k}$

2. $7\hat{i}+9\hat{j}+11\hat{k}$

3. $3\hat{i}+4\hat{j}+11\hat{k}$

4. $-3\hat{i}-4\hat{j}+11\hat{k}$

A candle is held \(3\) cm away from a concave mirror of focal length \(12\) cm, then the nature of the image formed by the mirror is:
1. real, inverted
2. virtual, erect
3. real, erected 
4. virtual, inverted

A plane mirror is placed at x = 0 along the y-axis and an object starts moving with velocity $\left(2\hat{i}+2\hat{j}\right)$ m/s from x = 3. Relative velocity of the image in the mirror with respect to the object is:

1.  4 m/s along the -x-axis

2.  4 m/s along the +x axis

3.  $2\sqrt{2}$ m/s making an angle of $45°$ with the +x axis

4.  $2\sqrt{2}$ m/s making an angle of $135°$ with the +x axis

The angle of minimum deviation for a glass prism of refractive index \(\mu = \sqrt{3}\) equals the refracting angle of the prism. The angle of the prism is:
1. \(30^{\circ}\)
2. \(60^{\circ}\)
3. \(90^{\circ}\)
4. \(45^{\circ}\)$$