A converging spherical wavefront is obtained from

(1) Light emerging from a convex lens when a point source is placed at its focus

(2) A parallel beam of light incident on the convex lens

(3) Light converging at a point

(4) Both (2) & (3)

A concave lens of glass of refractive index 1.5 has both surfaces of the same radius of curvature R. On immersion in a medium of refractive index 1.75, it will have as a

1. Divergent lens of focal length 3R

2. Divergent lens of focal length 4R

3. Convergent lens of focal length 3.5R

4. Convergent lens of focal length 5R

A ray is incident normally on a right-angled prism whose R.I is $\sqrt{3}$ and prism angle $\mathrm{A}=30°$. Deviation to the ray is equal to

(1) $\frac{\mathrm{\pi }}{2}$

(2) $\frac{\mathrm{\pi }}{6}$

(3) $\frac{3\mathrm{\pi }}{2}$

(4) 2$\mathrm{\pi }$

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:

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. $t\left(2-\frac{1}{\mu }\right)i$