Name: Sign Convention for Spherical Lenses
Uploaded: 2019-07-19
Duration: 3 min 25 s
Description: Do you know on which side of the lens we should keep the object? There are some conventions that specify things like this. Watch the video to find out what t...

Question

The figure shows a convex and a concave lens of focal lengths $+ 20 cm, - 30 cm$ respectively, their lenses in contact. What is the power of each lens? What is the focal length of the combined lens?

Accepted Answer

Give:

The focal length of the convex lens, $f_{1} = + 20 cm = + 0.2 m$ .

The focal length of the concave lens, $f_{2} = - 30 cm = - 0.3 m$ .

Let, $P_{1}$ be the power of the convex lens and $P_{2}$ be the power of the concave lens.

We know that, the power of the lens is given by, $P = \frac{1}{f}$ .

The power of the convex lens is $P_{1} = \frac{1}{f_{1}} = \frac{1}{0.2} = + 5 D$ .

And the power of the concave lens is $P_{2} = \frac{1}{f_{2}} = \frac{1}{- 0.3} = - 3.33 D$ .

We know that when the two or more thin lenses are put in contact the power of the combination is equal to the algebraic sum of powers of the lenses.

$P = P_{1} + P_{2} = + 5 + (- 3.33) = + 1.67 D .$ Thus, the power of the combination of lenses is $P = + 1.67 D$ .

Let, $f$ be the focal length of the combination.

We know that the focal length of the combination is $f = \frac{1}{P} f = \frac{1}{1.67} f = + 0.6 m = + 60 cm .$

Thus, the focal length of the combination is $f = + 60 cm$ .

The figure shows a convex and a concave lens of focal lengths $+ 20 cm, - 30 cm$ respectively, their lenses in contact. What is the power of each lens? What is the focal length of the combined lens?

Important Questions on Refraction Through a Lens

Learn and Prepare for any exam you want !

The figure shows a convex and a concave lens of focal lengths +20 cm, -30 cm respectively, their lenses in contact. What is the power of each lens? What is the focal length of the combined lens?

Important Questions on Refraction Through a Lens

Learn and Prepare for any exam you want !

The figure shows a convex and a concave lens of focal lengths $+ 20 cm, - 30 cm$ respectively, their lenses in contact. What is the power of each lens? What is the focal length of the combined lens?