A boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length \(10\) cm. The diameter of the sun is \(1.39\times 10^9~\text{m}\) and its mean distance from the earth is \(1.5\times 10^{11}~\text{m}.\) What is the diameter of the sun's image on the paper?
1. \( 9.2 \times 10^{-4}~\text{m} \)
2. \(6.5 \times 10^{-4}~\text{m} \)
3. \(6.5 \times 10^{-5}~\text{m} \)
4. \( 12.4 \times 10^{-4}~\text{m} \)

An object is placed in front of a concave mirror. The distance of the object from the focus is 10 cm and the distance of the image from the focus is 40 cm, then the focal length mirror is :

(1) 20 cm

(2) 10 cm

(3) 40 cm

(4) 30 cm

If the critical angle for a liquid A is 60$°$ and critical angle for the liquid B is 45$°$, then the critical angle for a ray traveling from A to B will be

(1) Less than 45$°$

(2) More than 60$°$

(3) Between 45$°$ and 60$°$

(4) Does not exist

If the plane surface of a planoconvex lens is silvered, then it will behave as :

(1) Converging mirror

(2) Diverging mirror

(3) Plane mirror

(4) May behave as (1) or (2)

Chromatic aberration of a lens can be corrected by

(1) Reducing its apperture

(2) Proper polishing of its surfaces

(3) Suitable combining it with another lens

(4) Providing different suitable curvature to its surfaces

A plane mirror is placed at the bottom of a fish tank filled with water of refractive index $\frac{4}{3}$. The fish is at a height 10 cm above the plane mirror. An observer O is situated vertically above the fish outside. The apparent distance between fish and its image for the observer is-

1.  15 cm

2.  30 cm

3.  35 cm

4.  45 cm

If one surface of a biconvex lens is silvered, then it behaves as

(1) A concave mirror of focal length $\frac{R}{4\mu -2}$

(2) A concave mirror of focal length $\frac{R}{2\mu }$

(3) A convex mirror of focal length $\frac{R}{4\mu -2}$

(4) A concave mirror of focal length $\frac{R}{2\mu -2}$

An astronomical telescope has an angular magnification of 20 in its normal adjustment. The focal length of the eyepiece is 4 cm. Distance between objective and eyepiece is :

1.  80 cm

2. 84 cm

3.  76 cm

4.  90 cm

A liquid of refractive index $\frac{4}{3}$ is placed between two identical planoconvex-lenses touching each other at their spherical surfaces of radius R. If the refractive index of the lens is 1.50, then the lens behaves

(1) Convergent with power P=$\frac{1}{3R}$

(2) Convergent with power P=$\frac{1}{6R}$

(3) Divergent with power P=$\frac{1}{3R}$

(4) Divergent with power P=$\frac{1}{6R}$