Question

 A 2 cm high object is placed at a distance of 20 cm from a concave mirror. A real image is formed at 40 cm from the mirror. The focal length of the mirror is

a) – 40cm

b) – 13cm

c) – 13.34cm

d) 13.34cm

​

Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• Height of object = 2 cm
• Object distance ( u ) = -20 cm
• Image Distance ( v ) = -40 cm

To Find:

• We have to find the focal length of given concave mirror

Solution:

Given that am object is placed at a distance of 20 cm from a concave mirror

$\boxed{\sf{Object \: Distance \: (u) = - 20 \: cm}}$

A real image is formed at a distance of 40 cm from concave mirror

$\boxed{\sf{Image \: Distance \: (v) = - 40 \: cm}}$

We have to find the focal length of mirror

$\sf{ }$

$\odot \:$Using Mirror Formula :

$\implies \boxed{\sf{\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}}}$

Where the variables have their usual meaning

$\implies \sf{\dfrac{1}{-40} + \dfrac{1}{-20} = \dfrac{1}{f}}$

$\implies \sf{- \dfrac{1}{40} - \dfrac{1}{20} = \dfrac{1}{f}}$

Taking LCM on LHS

$\implies \sf{\dfrac{-1-2}{40}= \dfrac{1}{f}}$

$\implies \sf{\dfrac{-3}{40}= \dfrac{1}{f}}$

Reciprocating Both Sides

$\implies \sf{f = - \dfrac{40}{3}}$

$\implies \boxed{\sf{f = - 13.34 \: cm }}$

Hence Option C is Correct

________________________________

$\huge\underline{\sf{\red{A}\orange{n}\green{s}\pink{w}\blue{e}\purple{r}}}$

$\large\boxed{\sf{Focal \: Length = - 13.34 \: cm}}$

_________________________________

Nature of image formed :

• Real and Inverted
• Magnified
• In front of concave mirror

Answer 2

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