A lens having focal length f and aperature of diameter d forms an image of intensity I. Aperture of diameter $\frac{d}{2}$ in central region of lens is covered by a black paper. Focal length of lens and intensity of image now will be respectively

(a) f and $\frac{1}{4}$                                      (b) $\frac{3f}{4}and \frac{I}{2}$

(c) f and $\frac{3I}{4}$                                     (d) $\frac{f}{2}and \frac{I}{2}$

A ray of light is incident on a $60°$ prism at the minimum deviation position. The angle of refraction at the first face (ie, incident face) of the prism is 

(1) $\mathrm{zero}$                                             

(2) $30°$

(3) $45°$                                               

(4) $60°$

Two thin lenses of focal length $f_1 and f_2$ are in contact and coaxial. The power of the combination is 

(1) $\sqrt{\frac{f_1}{f_2}}$                   

(2) $\sqrt{\frac{f_2}{f_1}}$

(3) $\frac{f_1-f_2}{f_1{f}_2}$               

(4) $\frac{f_1+f_2}{f_1{f}_2}$

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)