Question

The radius of curvature of both the surfaces of a double convex lens is R. The refractive index of the material of the lens is 1.5. When a point-source of light is placed on the principal axis of the lens at a distance of 20 cm in-front of the one surface of the lens, then rays emerge from the other surface normally. Determine the radius of curvature R of each surface of the lens.        

Solution

Correct option is

40 cm

 

A point-source O is placed at a distance of 20 cm in front of the lens. The rays emerging normally from the second surface of the lens will appear to come from the centre of curvature C2 of the second surface, as shown. Thus, C2 is virtual image of the source O. Now, for the lens, we have

u = –20cm and v = –R. The lens formula is   

                      

Putting the above values of u and v. we have

               

  

or                  R = 40 cm.

SIMILAR QUESTIONS

Q1

In Young’s double slit experiment using two identical slits, the intensity of the maximum at the centre of the screen is I. What will be the intensity at the centre of the screen if one of the slits is closed?   

Q2

Glycerine (refractive index 1.4) is poured into a large jar of radius 0.2 m to a depth of 0.1 m. There is a small light source at the centre of the bottom of the jar. Find the area of the surface of glycerine through which the light passes.  

Q3

A ray of light travelling in glass (refractive index, ang = 3/2) is incident on a horizontal glass-air surface at the critical angle c. If a thin layer of water (refractive index, anw = 4/3) is now poured on the glass-air surface, at what angle will the ray of light emerge into air at the water-air surface?

Q4

The radius of curvature of the convex surface of a thin plano-convex lens is 20 cm. Refractive index of the medium of the lens is 1.5. Calculate the focal length of the lens.   

Q5

The thickness of a plano-convex lens is 4 cm. When it is placed on a horizontal table in such a way that its curved surface be in contact with the table, then the depth of a bottom-point of the lens appears 3 cm. If the lens is inverted so that its plane surface be in contact with the table, then the apparent depth of the centre of the lens-surface is found to be (25/8) cm. Determine the focal-length of the lens.     

Q6

The focal length of a convex lens in air is 20 cm. What will be its focal length if it is immersed in a liquid of refractive index 1.35? Refractive index of glass is 1.50.  

Q7

A lens made of glass having refractive index 1.5 has a focal length of 50 cm in air. What will be its focal length if it is immersed in a liquid of refractive index 1.2?  

Q8

A convex lens of glass (refractive index 1.5) has both surfaces of radius of curvature 20 cm. Find its focal length and nature when it immersed in a liquid of refractive index 1.75. 

Q9

The focal length of a lens of glass (n = 1.5) in air is 0.4 m and in a liquid is 1.2m. Determine the refractive index of the liquid.

Q10

An air passenger sitting in an aeroplane flying at a height of 2000 meter from the earth takes photographs of the earth. The focal-length of his camera-lens is 50 cm. The size of the camera-film is (18 × 18)cm2. What maximum area can be covered by the camera?