A convex lens forms the image of a point object \(O\) on the screen. If a glass slab of thickness 3 cm and refractive index 1.5 is put as shown below, then to have the image of the object on the screen, the object should be shifted:

  

1.	away from the lens by 1 cm
2.	away from the lens by 1.5 cm
3.	towards the lens by 1 cm
4.	towards the lens by 1.5 cm

Two convex lenses of focal lengths $f_1 and f_2$ are separated co-axially by a distance d. The power of the combination will be zero if d equals to

1. $\sqrt{f_1{f}_2}$

2. $f_1+f_2$

3. $\frac{f_1-f_2}{2}$

4. $\frac{f_1+f_2}{2}$

In the following diagram what is the distance x if the radius of curvature R=15 cm?

(1) 30 cm

(2) 20 cm

(3) 15 cm

(4) 10 cm

A thin equiconvex lens of power P is cut into three parts A, B, and C as shown in the figure. If $P_1, P_2 \mathrm{and} P_3$ are powers of the three parts respectively, then 

1.  $P_1 = P_2 = P_3$

2.  $P_1 > P_2 = P_3$

3.  $P_1 < P_2 = P_3$

4.  $P_2 = P_3 = 2P_1$

In the diagram shown below, the image of the point object O is formed at l by the convex lens of focal length 20 cm, where $F_1 and F_2$ are foci of the lens. The value of x' is

(1) 10 cm

(2) 20 cm

(3) 30 cm

(4) 40 cm

An astronomical telescope has angular magnification of 40 in its normal adjustment. If focal length of eyepiece is 5 cm, the length of the telescope is:
1. 190 cm
2. 200 cm
3. 205 cm
4. 210 cm

In case of refraction through a glass slab, if i is very small, the lateral shift is (t is thickness, u is the refractive index)

1. $t\left(1+\frac{1}{\mu }\right)i$

2. $t\left(1-\frac{1}{\mu }\right)i$

3. $t\left(2+\frac{1}{\mu }\right)i$

4. $t\left(2-\frac{1}{\mu }\right)i$

The angle of a distant object formed at the objective of a telescope is 2 minutes. If the focal length of objective and eyepiece of the telescope is 200 cm and 20 cm, then the size of the image formed by the objective is approximately

1.  20 cm

2.  0.12 cm

3.  0.4 cm

4.  12 cm

The focal length of a convex lens is 40 cm and the size of the inverted image formed is half of the object. The distance of the object is:

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