A point object O is placed at distance 20 cm from a biconvex lens of radius of curvature 20 cm and $\mu$=1.5. The final image produced by lens and mirror combination will be at

(1) 10 cm from the mirror

(2) 20 cm from lens

(3) -20 cm from lens

(4) -15 cm from the mirror

If the angle of a triangular prism is A and the refractive index of the material is $\mu$, then under what condition will there be no emergent ray?

1.  $A = 2 {\sin }^{-1}\left(\frac{1}{\mu }\right)$

2.  $A < 2 {\sin }^{-1}\left(\frac{1}{\mu }\right)$

3.  ${\sin }^{-1}\left(\frac{1}{\mu }\right) < A < 2 {\sin }^{-}\left(\frac{1}{\mu }\right)$

4.  $A > 2 {\sin }^{-1}\left(\frac{1}{\mu }\right)$

A thin lens whose power is +2D is cut into two pieces perpendicular to the principal axis. The focal length of each part will be

(1) 1 m

(2) 0.1 m

(3) 75 cm

(4) 0.05 m

A light ray is incident at an angle of $60°$ on one face of a  prism of a refractive angle $90°$. If light ray grazes the second face, then the refractive index of the material of prism is-

1. $\sqrt{\frac{3}{2}}$

2. $\sqrt{2}$

3. $\sqrt{\frac{5}{2}}$

4. $\frac{\sqrt{7}}{2}$

The near point of a hypermetropic eye is \(1~\text{m}.\)What is the power of the lens required to correct this defect?
1. \(-3~\text{D}\)
2. \(+3~\text{D}\)
3. \(+1~\text{D}\)
4. \(-1.75~\text{D}\)

The minimum magnifying power of an astronomical telescope is \(40\). If the length of the telescope is \(205\) cm, then the focal length of its field lens is:
1. \(5\) cm
2. \(200\) cm
3. \(40\) cm
4. \(140\) cm

A boy with defective eye-sight cannot see things beyond 50 cm. The corrective lens required has the power:

1. +1 D

2. +2 D

3. -1 D

4. -2 D

The focal lengths of the objective and eyepiece of a terrestrial telescope are 50 cm and 10 cm respectively. The magnifying power of the telescope when the final image is formed at infinity is

(1) 3.75

(2) -2.5

(3) -4.25

(4) +5

A convex mirror of focal length \(20~\text{cm}\) forms an image that is a quarter of the object's size. The distance of the object from the mirror is:
1. \(50~\text{cm}\)
2. \(-60~\text{cm}\) 
3. \(-40~\text{cm}\) 
4. \(-70~\text{cm}\)

The focal length of a thin convex lens for red and blue light is 0.5m and 0.484m.  The dispersive power of the lens is 

1. 0.984

2. 0.032

3. 0.484

4. 0.434