Question

An object placed 20 cm infront of a mirror is found to have an image of 15 cm in front of it. find the focal length of the mirror. And the kind of mirror​

Answer 1

Given :

• Object distance ( u ) = - 20 cm
• Image distance ( v ) = - 15 cm

Note - The negative sign here implies ‎that the image is formed in front of the mirror.

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To find :

• Focal length of the mirror
• The kind of the mirror

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Concept :

From mirror formula we know that ,

$\bf\dag\:\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

where, f denotes focal length , v denotes image distance and u denotes object distance.

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Solution :

Using the formula -

$\bf\:\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

Substituting the given values -

$\sf\implies\:\frac{1}{f}=\frac{1}{(-15)}+\frac{1}{(-20)}$

$\sf\implies\:\frac{1}{f}=-\frac{1}{15}-\frac{1}{20}$

$\sf\implies\:\frac{1}{f}=-\frac{-4-3}{60}$

$\sf\implies\:\frac{1}{f}=-\frac{-7}{60}$

$\small{\underline{\boxed{\mathrm{\implies\:f=\frac{-60}{7}}}}}$

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Thus the focal length of the mirror is $\small{\mathfrak\red{\frac{60}{7}~cm}}$ .

Image is formed in front of the mirror hence the mirror is $\tt\:concave$.

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Know more about mirror :

• $\sf\:What~is~a~mirror~?$

➻ Simply a mirror is a surface which reflects the image of an object.

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• $\sf\:Types~of~mirror~:$

➻ Two types of mirror are there. These are :

⠀⠀⠀⌬ Convex mirror, and

⠀⠀⠀⌬ Concave mirror

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• $\sf\:What~is~a~convex~mirror~?$

➻ A spherical mirror whose reflecting surface is curved outwards is called a convex mirror.

It is also known as diverging mirror, since a parallel beam of light falling on this mirror appears to diverge from a point after reflection.

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• $\sf\:What~is~a~concave~mirror~?$

➻ A spherical mirror whose reflecting surface is curved inwards is called a concave mirror.

It is also known as converging mirror, since a parallel beam of light falling on this mirror appears to converges from a point after reflection.

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