A plane-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices in  μ₁ and μ₂ and R is the radius of curvature of the curved surface of the lenses. then the focal length of the combination is

(1) R/2(μ₁₊μ₂₎

(2) R/2(μ_1-μ₂₎

(3) R/(μ_1-μ₂₎

(4) 2R/(μ2-μ₁₎

When a biconvex lens of glass having refractive index 1.47 is dipped in a liquid, it acts as a plane sheet of glass. This implies that the liquid must have refractive index 

(1)equal to that of glass

(2)less than one

(3)greater than that of glass 

(4)less than that of glass

A ray of light is incident at an angle of incidence, i, on one face of a prism of angle A (assumed to be small) and emerges normally from the opposite face.If the refractive index of the prism is $\mu ,$ the angle of incidence i, is nearly equal to

(1)$\mu A$                                   

(2)$\frac{\mu A}{2}$

(3)$A/\mu$                                 

(4)$A/2\mu$

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

(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

A biconvex lens 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

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) $\frac{3f}{4}and<mspace\; width="1em"></mspace>\frac{I}{2}$

(c) f and $\frac{3I}{4}$                                     (d) $\frac{f}{2}and<mspace\; width="1em"></mspace>\frac{I}{2}$