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) $\frac{f}{2}and \frac{I}{2}$

The speed of light in media ${\mathrm{M}}_1$ and ${\mathrm{M}}_2$ is $1.5\times {10}^8 \mathrm{m}/\mathrm{s}$ and $2.0\times {10}^8 \mathrm{m}/\mathrm{s}$ respectively. A ray of light enters from medium ${\mathrm{M}}_1$ to ${\mathrm{M}}_2$ at an incidence angle i. If the ray suffers total internal reflection, the value of i is

(1) equal to ${\sin }^{-1}\left(\frac{2}{3}\right)$

(2) equal to or less than ${\sin }^{-1}\left(\frac{3}{5}\right)$

(3) equal to or greater than ${\sin }^{-1}\left(\frac{3}{4}\right)$

(4) less than ${\sin }^{-1}\left(\frac{2}{3}\right)$

A ray of light is incident on a $\mathrm{}$\(60^\circ\) prism at the minimum deviation position. The angle of refraction at the first face (ie, incident face) of the prism is:
1. zero
2. \(30^\circ\)
3. \(45^\circ\)
4. \(60^\circ\)

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 ray of light traveling in a transparent medium of refractive index $\mu$ falls, on a surface separating the medium from the air at an angle of incidence of 45$°$. For which of the following values of $\mu$ the ray can undergo total internal reflection?

1. $\mu =1.33$                             

2. $\mu =1.40$

3. $\mu =1.50$                             

4. $\mu =1.25$

A converging beam of rays is incident on a diverging lens. Having passed though the lens the rays intersect at a point 15cm from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5cm closer to the lens. The focal length of the lens is:

(1) -10cm                                   

(2) 20cm

(3) -30cm                                   

(4) 5cm

A thin prism of angle $15°$ made of glass of refractive index ${\mathrm{\mu }}_1=1.5$ is combined with another prism of glass of refractive index ${\mathrm{\mu }}_2=1.75.$ The combination of the prism produces dispersion without deviation. The angle of the second prism should be 

(1) $7°$                                             

(2) $10°$

(3) $12°$                                             

(4) $5°$

Which of the following is not due to total internal reflection?

(1) Difference between apparent and real depth of a pond

(2) Mirage on hot summer days

(3) Brilliance of diamond

(4) Working of optical fibre

A biconvex lens of refractive index 1.5, has a radius of curvature of magnitude 20 cm. Which one of the following options describes best the image formed of an object of height 2 cm placed 30 cm from the lens?

(1) Virtual, upright, height=0.5 cm

(2) Real, inverted, height=4 cm

(3) Real, inverted, height=1 cm

(4) Virtual, upright, height=1 cm