Question

in an optical instrument a convex lens of focal length 20cm is used in combination with the concave lens of focal length 40 cm what is the power of this combination

Answer 1

1/f1 + 1/f2 = 1/f f1=0.2m ,f2= -0.4m 1/f=10/4 power of combination=2.5D

Answer 2

Answer:

The power of lens is 2.5 D (diopter)

Step-by-step explanation:

The power of a lens is the reciprocal of its focal length in meters,

That is,

D = $\frac{1}{F}$

where D is the power in diopters and

F is the focal length in meters

Now,

We are given convex lens of focal length = 20 cm

Focal length of convex length = 0.2 m [ 1 cm = 0.01 m ]

Similarly,

We are given concave lens of focal length = 40 cm

Focal length of concave lens = - 0.4 m [ 1 cm = 0.01 m ]

( We always take focal length of concave lens as negative )

Since we know,

Focal length is calculated as :

$\frac{1}{F}$ =  $\frac{1}{f_{1} }$+  $\frac{1}{f_{2} }$

$\frac{1}{F}$ =  $\frac{1}{0.2}$ +  $\frac{1}{(- 0.4 )}$

$\frac{1}{F}$ =  $\frac{1}{0.2}$ -  $\frac{1}{( 0.4 )}$

$\frac{1}{F}$ =  $\frac{1}{0.2}$ -  $\frac{1}{( 0.4 )}$

$\frac{1}{F}$ =  $\frac{0.4 - 0.2}{0.08 }$  =  $\frac{0.2}{0.08 }$

$\frac{1}{F}$ = 2.5

As we know,

D =  $\frac{1}{F}$

Hence,

D = 2.5 diopters