Question

A small object is placed at a distance of 15 cm from two coaxial thin lenses in contact. The focal length of each lens is 25 cm. What will be the distance between the object and its image when both the lenses are (i) convex, (ii) concave. 

Solution

Correct option is

90 cm, 8.2 cm

 

(i) If F is the focal length of the combination, then

                            

Here f1 = f2 = +25 cm (both the lenses are convex). Therefore,

                              

                         

If the image is at a distance v from the combination of lenses, then

                         

Here u = –15 cm, F = +12.5 cm.   

                     

                      

The object is at a distance of 15 cm on one side and the image is at a distance of 75 cm on the other side of the lens-combination. Hence the distance between the object and the image is

                       15 cm + 75 cm = 90 cm.

(ii) When both the lenses are concave (f1 = f2 = –25 cm), then F = – 12.5 cm. Again, by the lens formula 

                       

  

                   

Now the image is on the same side of the lens as the object. Hence the distance between the object and the image is

                     15 cm – 6.8 cm = 8.2 cm.

SIMILAR QUESTIONS

Q1

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.   

Q2

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.     

Q3

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.  

Q4

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?  

Q5

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. 

Q6

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.

Q7

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.        

Q8

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?      

Q9

The diameter of sun is 1.4 × 109 meter. Determine the diameter of the image of the sun formed by a convex-lens of focal length 1.0 meter. Distance of the sun from the earth is 1.0 × 1011 meter. 

Q10

The image of an object is formed at a distance of 40 cm from the object, when the lens is placed exactly mid-way between the object and the image. What is the power of the lens?