Question

The power of a combination of two lenses X and Y is 5 D. If the focal length of lens X be 15 cm :
(a) calculate the focal length of lens Y.
(b) state the nature of lens Y.

 

Answer 1

(a) The focal length of lens X, ie., f₁ = 15 cm = 0.15 m
     Power of lens X, `p_-1=1/f_1=1/0.15=6.67` D
Let the power and the focal length of the lens Y be P₂ and f_2^, respectively.
The resultant power of the combination of two lenses is the algebraic sum of the powers of the individual lenses.
∴ Power of combination of lenses P = P₁ + P₂
                                  ⇒5 = 6.67 + P₂
​                               ⇒P₂ = 5 - 6.67 = - 1.67 D
The power of the lens is related to the focal length of the lens as:   

`p_2=1/f_2` 

`-1.67=1/f_2`  

`f_2=1/-1.67=0.60`m=-60cm 

`f_2=1/-1.67=-0.60m=-60cm` 

The focal length of the lens Y is -60 cm.

(b) The focal length of the lens Y is negative. Therefore, the lens is concave and diverging in nature.