The angle of a prism is A. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index μ of the prism is

(1)2sinA

(2)2cosA

(3)1/2cosA

(4)tanA

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 \(\mu_1\) and \(\mu_2\) and \(R\) is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is:

For a normal eye, the cornea of eye provides a converging power of 40 D and the least converging power of the eye lens behind the cornea is 20 D. Using this information, the distance between the retina and the cornea-eye lens can be estimated to be

(1) 5 cm

(2) 25 cm

(3) 1.67 cm

(4) 1.5 cm

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. \(\dfrac{\mu A}{2}\) 
3. \(\frac{A}{\mu}\)
4. \(\frac{A}{2\mu}\)                                 

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 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