Question

A real image is formed by a lens at a distance of 20 cm from the lens. The image shifts towards the combination by 10 cm when a second lens is brought in contact with the first lens. Determine the power of the second lens.   

Solution

Correct option is

5 dioptre

 

The image formed by the lens is ‘real’. Hence the lens in convex. Let its focal length be f1. Suppose the object is at a distance u from the lens, and the image is formed on the other side at a distance v (= 20 cm). From the lens formula    

                  

Let the focal length of the other lens be f2. Since on placing it in contact of the first lens, the image shifts 10 cm ‘nearer’ the lens-combination, the second lens also is convex. If the focal length of the combined lens be F, then  so again by the lens formula, we have

                  

By eq. (i) and (ii), we get         

                  

SIMILAR QUESTIONS

Q1

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?  

Q2

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. 

Q3

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.

Q4

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.        

Q5

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?      

Q6

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. 

Q7

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. 

Q8

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?

Q9

Two lenses of powers +2.50 D and –3.75 D are combined to form a lens combination. Determine the focal-length of this combination.  

Q10

Two lenses of powers +12 D and –2D are placed in contact. This combination is placed between an object and a screen which are 60 cm apart. If this combination is kept in two positions between object and screen, a real image of the object is formed on the screen. Calculate the distance between the two positions of the combination.