Question

An object of size 5 cm is placed at 20 cm in front of convex lens of focal length 15 cm. At what distance from the lens should a screen be placed so that a sharp image can be obtained? Find the size and nature of the image.

Answer 1

it should be kept at a distance 60 cm .The size will be 10 cm and nature real,inverted and enlarged

Answer 2

The image will be formed at a distance of 60 cm from the mirror.  

Explanation:

It is given that,

Height of the object, h = 5 cm

Object distance, u = -20 cm  

Focal length of the convex lens, f = +15 cm (for convex mirror it is positive)

Let the object is placed at a distance of v from the lens. It can be calculated using mirror's formula as :

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

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

$\dfrac{1}{v}=\dfrac{1}{15}+\dfrac{1}{(-20)}$

v = 60 cm

So, the image will be formed at a distance of 60 cm from the lens. Hence, this is the required solution.

Magnification,

$m=\dfrac{v}{u}=\dfrac{h'}{h}$

h' is the size of image

$h'=h\dfrac{v}{u}$

$h'=5\times \dfrac{60}{-20}$

h' = -15 cm

So, the size of image is 15 cm and it is inverted. Hence, this is the required solution.

Learn more,

Mirror's formula

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