Power of Combination of Lenses


 
 
Concept Explanation
 

Power of Combination of Lenses

Power of Lens: 

The power of a lens is defined as the reciprocal of its focal length.

P=frac{1}{f} 

Here SI unit for the focal length is meters. The S.I. unit of power is diopter(D).

Power of Combination of Lens:

When two or more thin lenses are kept in contact with each other such that they have the same principal axis, then the power of the combination is treated as a single thin lens.The power of this combination is equal to the algebraic sum of powers of individual lenses i.e.

    P=P_1+P_2+.......P_n.

When two or more thin lenses are used in combination, the equivalent focal length (f) can be calculated as the reciprocal of the resultant power of the combination (P). The focal length F of the equivalent single lens is given by:

F=frac{1}{P}

Let us take the case of two lenses of focal length f_1 and f_2 . The power of these lenses be P_1 and P_2. Then

P=P_1+P_2

frac{1}{F}=frac{1}{f_1}+frac{1}{f_2}

Rightarrow frac{1}{F}=frac{f_1+f_2}{f_1f_2}

Rightarrow F= frac{f_1f_2}{f_1+f_2}

This equation is often used in deciding the power of lens to be prescribed for a person suffering a vision defect

Illustration:  If by using two lenses of power +1.5 D and +1.0 D in contact the person can see properly, then find power of the lens prescribed to the person.

Solution: Given power of two lenses

P_1= + 1.5 ;D

P_1= + 1.0 ;D

then power of the combination will be:

P=P_1+P_2

P=+ 1.5+1.0 = +2.5; D

A combination of lens power +2.50 D is prescribed to the person.

Uses of Combination of Lenses:

1. The use of combination of lenses increases the sharpness of image, the image produced is also free from many defects.

2.  The additive property of the powers of the lenses can be used to design lens systems to minimise certain defects in images produced by a single lens. Such a lens system, consisting of several lenses in contact, is commonly used in designing of camera lenses and the objectives of microscopes and telescopes.

Sample Questions
(More Questions for each concept available in Login)
Question : 1

Power of a lens is defined as ______________________.

Right Option : B
View Explanation
Explanation
Question : 2

The SI unit of power is ____________________ .

Right Option : C
View Explanation
Explanation
Question : 3

Which of the following are correct ?

(a) The power of a lens is defined as the reciprocal of its focal length.

(b) The use of combination of lenses increases the sharpness of image, the image produced is also free from many defects.

Right Option : B
View Explanation
Explanation
 
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