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

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:

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 converging beam of rays is incident on a diverging lens. Having passed through the lens the rays intersect at a point \(15~\mathrm{cm}\) from the lens on the opposite side. If the lens is removed the point where the rays meet will move 5 cm closer to the lens. The focal length of the lens is:

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:

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) $60°$