Question

An object is placed at a distance of 24cm from
a convex lens of focal length 10cm, when an
image is obtained on the other side of the lens.
Calculate the distance of the screen from the
lens?​

Answer 1

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Answer 2

Given: A convex lens

focal length = f = 10 cm

object distance = u = 24 cm

To find: Distance of the screen from the lens

Solution:

A screen is placed to obtain images on it in case of real images. Hence, the screen has to be placed at a distance equal to the image distance.

To find image distance, let us apply the lens formula. Here, the focal length is positive as the lens is a convex lens.

The lens formula is given below:

$\frac{1}{f} =\frac{1}{u} +\frac{1}{v}$

$\therefore \frac{1}{v} = \frac{1}{f} -\frac{1}{u}$

$\therefore \frac{1}{v} = \frac{1}{10} -\frac{1}{24}$

$\therefore \frac{1}{v} = \frac{12-5}{120}$

$\therefore \frac{1}{v} = \frac{7}{120}$

$\therefore 7v= 120\\ \\\therefore v = \frac{120}{7} \\ \\\therefore v = 17.14 \:cm$

Thus the image will be formed at 17.14 cm distance away from the optical centre of the lens. Hence, screen is to be placed at 17.14 cm.

Answer:

The distance of the screen from the lens is calculated and it will be 17.14 cm.