Question

A convex lens forms a real and inverted image of a
needle at a distance of 50 cm from it. Where is the
needle placed in front of the convex lens if the image is
equal to the size of the object? Also, find the power of
the lens.​

Answer 1

Answer:

Object distance = - 50 cm

Power of lens = +0.04 D OR +1/25 D

Explanation:

Given:

size of image = size of object

From the 6 cases of convex lens image formation, we know that when object is at 2F1 the image is formed at 2F2 and the object and image sizes are equal.

Therefore, object is at - 50cm.

( since, 2F2 = +50cm, therefore 2F1 = - 50cm)

Power Of lens

Since 2F = 50 cm

therefore F (focal length) = 50/2 = 25cm.

We know

P = 1/ F

= 1/25 D.

Answer 2

Hey Happy Soul ❤

Your Answer :

The position of image should be at 2F, since the image is real and same size.

It is given that the image of the needle is formed at a distance of 50 cm from the convex lens.

Therefore, the needle is placed in front of the lens at a distance of 50 cm.

Focal length :

Object distance (u) = - 50 cm

Image distance, (v) = 50 cm

Focal length = f

According to the lens formula,

1/v - 1/u = 1/f

1/f = 1/50 - 1/(-50)

1/f = 1/50 + 1/50

1/f = 1/25

f = 25 cm = 0.25 m

Power of lens :

p = 1 / f ( in meter)

p = 1/0.25 = +4 D

Hope this will helps you ☺

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