Question

What is the focal length of convex lens of focal length 30 cm in contact with a concave lens of focal length 20cm
Is the system diverging or converging..​

Answer 1

Answer :

Let the focal length be f .

Focal length of convex is positive .

Focal length of concave is negative .

Given :

$f_1=30cm\\\\f_2=-20cm$

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}\\\\\implies \frac{1}{f}=\frac{1}{f_1}-\frac{1}{f_2}[\therefore\:f_2\:is\:negative]\\\\\implies \frac{1}{f}=\frac{1}{30}-\frac{1}{20}\\\\\implies \frac{1}{f}=\frac{2-3}{60}\\\\\implies \frac{1}{f}=-\frac{1}{60}$

Since the focal length is negative , it has to be a concave lens .

Focal length of the concave lens is 60 cm .

The lens is a diverging lens as concave lens always diverges the given rays through its principal axis.

Answer 2

Given,

Focal length of convex lens= 30cm

let it be f1 = 30cm

Focal length of concave lens = 20cm

Let it be f2= (-20cm)

REMEMBER

1)The focal length of CONVEX LENS is always positive.

2)The focal length of CONCAVE LENS is always negetive.

Now, we know=>

Total focal length of the combination of lens will be=>

1/F = 1/f1 + 1/f2

where '1/F' is the combined focal length of lens.

=>1/F = 1/30 - 1/20

=>1/F = (2-3)/60

=>1/F = -1/60

=>F = -60 cm

Since the combined focal length of the lens is negetive, hence the combination behaves as a CONCAVE LENS

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