Question

5. A convex lens forms a real and inverted image of a needle
is the needle placed in front of the convex lens if the image
Also, find the power of the lens.​

Answer 1

A convex lens forms a real,inverted image of the same size as that of the object ,if the object is placed at 2F1.

In this case v=+50cm and m=-1

Now,m=v/u

u=v/m=50/-1=-50cm

Here,v=2f=50cm

f=50cm/2=25cm

               =o.25m

Power p =1/f(m)

               =1/0.25m

               =100/25m-1

               =4 dioptre

               =4 D

  Thus, the needle is placed at 50cm from the convex lens of power 4 D.

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 !!