Question

a convex lens forms a real and inverted image of a needle a distance of 50cm from it. Where is the needle placed in front of the convex len if the image is equal to the size of objects? also, find the power of lens?

Answer 1

Answer: It is given that the image is real and inverted , so the sign convention is that only hi and u is neagtive.

Also the size of the image and the size of object is said to be equal,

This can happen only when object is at 2f and image formed at 2f.

V= 50

U=-50

So object to be placed 50 cm in front..

C=2f

C/2= f

50/2=f

25= f

P=1/f

P= 1/25

= .4

=.004 D

Explanation:

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,

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

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

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

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

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

Hope it Helps !!