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.

⚠NO SPAMS ALLOWED........❌

Answer 1

image will be placed at the distance of 50 cm from the convex lens and the power of the lens is + 4 diopter

Answer 2

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The position of the image should be at 2F since the image is the 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.

Object distance (u) = – 50 cm

Image distance, (v) = 50 cm

Focal length = ( f )

According to the lens formula,

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

$\frac{1}{f} = \frac{1}{50} - \frac{1}{ - 50}$

$= > \frac{1}{50} + \frac{1}{50} = \frac{1}{25}$

$f = 25cm \: = 0.25m \:$

$power \: of \: lens \: = \frac{1}{f(in \: metres \: )} = \frac{1}{0.25} = \: + 4d$

• Hence , the power of the lens = +4D

Hope it Helps !!