Question

An achromatic convergent lens combination is made by keeping in contact a convex lens of focal length 20 cm and a concave lens of focal length 30 cm. Dispersive power of the material of convex lens is 0.18. Find the dispersive power of the material of the concave lens, and the focal length of the combination.  

Solution

Correct option is

0.27, + 60

 

(i) The condition for achromatism of two lenses in contact is

                        

  

where f and f’ are the mean focal lengths of the lenses and ω and ω are the respective dispersive powers of the material of the lenses.

  

       

(ii) If F is the focal length of the lens-doublet, then

                        

        

As the focal length of the doublet is positive, it will behave as a convex lens.  

SIMILAR QUESTIONS

Q1

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. 

Q2

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?

Q3

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.   

Q4

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.  

Q5

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.  

Q6

The refractive indices of the material of a lens for yellow and red colours are 1.54 and 1.51 respectively. The focal length of the lens for yellow light is 34.0 cm. Calculate the focal length of the lens for red light.  

Q7

The refractive indices of the material of a lens for violet and red colours are 1.56 and 1.54 respectively. If the focal length of the lens for violet light is 40 cm, then calculate (i) focal length of the lens for red light. (ii) Longitudinal chromatic aberration of the lens and (iii) Dispersive power of the material of the lens.  

Q8

The refractive indices of the material of a lens for violet, yellow and red colours of light are respectively 1.66, 1.64 and 1.62. The mean focal length of the lens is 10 cm. Determine the chromatic aberration of the lens between the violet and the red colours.     

Q9

The dispersive powers of crown and flint glasses are 0.02 and 0.04 respectively. Find the focal length of the convex lens of crown glass which forms achromatic doublet with a concave lens of flint glass of focal length 80 cm.  

Q10

For an achromatic combination of lenses, the ratio of dispersive powers of materials used in lenses is 2:3. One lens has focal length equal to 10 cm. Find focal length, power and nature of second lens.