Question

The focal length of an achromatic combination of two lenses is 60 cm. If the ratio of the dispersive powers of the two lenses is 5/3, then find out the focal length of the two lenses.  

Solution

Correct option is

f = – 40 cm, f’ = 24 cm.

 

For achromatic lens-combination, we have  

                           

In achromatic (convergent) lens-combination the glass of convex lens is of less dispersive power, and the glass of concave lens is of more dispersive power. Here dispersive powers are in the ratio 5:3. Hence first lens (f) is concave and second lens (f’) is convex.

Substituting ω/ω = 5/3 in the above eq., we get

                              

  

Let the focal length of the lens-combination be F. Then

                              

From eq. (i):

                              

or                                 f’ = 24 cm.

Putting this value in eq. (i):   

                                   f = – 40 cm.

SIMILAR QUESTIONS

Q1

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.  

Q2

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.  

Q3

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.  

Q4

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.  

Q5

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.     

Q6

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.  

Q7

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.  

Q8

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.   

Q9

An achromatic objective lens of a telescope is made of two lenses of crown and flint glasses. If the dispersive powers of crown and flint glasses are 0.02 and 0.03, and the focal length of the lens made from crown glass is 16.0 cm, find the focal length of the lens made of flint glass. Also find the focal length of the combination. 

Q10

An achromatic combination of objective lens of a telescope is made of crown and flint glasses. Focal length of the combination is 0.25 meter. If the dispersive powers of crown and flint glasses are 0.02 and 0.03 respectively, then find the power of each lens of the combination.