A concave mirror of focal length $f_1$ is placed at a distance of d from a convex lens of focal length $f_2.$ A beam of light coming from infinity and falling on this convex lens concave mirror combination returns to infinity. The distance d must be equal to-

(1)$f_1+f_2$                                 

(2)$-f_1+f_2$

(3)$2f_1+f_2$                               

(4)$-2f_1+f_2$

The magnifying power of a telescope is 9. When it is adjusted for parallel rays the distance between the objective and eyepiece is 20cm. The focal length of lenses are 

(1) 10cm,10cm

(2) 15cm,5cm

(3) 18cm,2cm

(4) 11cm,9cm

For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index

(1) lies between $\sqrt{2}$ and 1

(2) lies between 2 and $\sqrt{2}$

(3) is less than 1

(4) is greater than 2

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

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 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) $5°$

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 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 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) $\frac{f}{2}and \frac{I}{2}$