Question

A 5 cm long needle is placed 10 cm from a convex mirror of focal length 40 cm. Find the natural and position and size of image

Answer 1

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Answer 2

Given that,

Size of needle, h = 5 cm

Object distance, u = -10 cm

Focal length of the focal length, f = 40 cm

To find,

The nature, position and size of image.

Solution,

Using mirror's formula :

$\dfrac{1}{f}=\dfrac{1}{v}+\dfrac{1}{u}\\\\\dfrac{1}{v}=\dfrac{1}{f}-\dfrac{1}{u}\\\\\dfrac{1}{v}=\dfrac{1}{(40)}-\dfrac{1}{(-10)}\\\\v=8\ cm$

The image will form at a distance of 8 cm. Formed image is virtual and erect.

Magnification:

$m=\dfrac{-v}{u}\\\\m=\dfrac{-8}{-10}\\\\m=0.8$

Also,

$m=\dfrac{h'}{h}\\\\h'=m\times h\\\\h'=0.8\times 5\\\\h'=4\ cm$

Size of image is 4 cm.

Learn more,

Mirror's formula

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