Question

A flame of lamp is 0.03m in length and is placed at a distance of 3m from a wall. At what ditance should the concave mirror be placed from the lamp to obtain a magnification of 3 . Also find the focal length
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Answer 1

Given :

Height of flame = 0.03m

Distance of object = 3m

Type of mirror : concave

Magnification = 3

To Find :

Distance of image and focal length of the mirror.

Solution :

❇ First we need to find distance of image in order to find focal length of the mirror.

Formula of magnification for concave mirror is given by

• m = -v/u

v denotes distance of image

u denotes distance of object

By substituting the values;

➠ m = -v/u

➠ 3 = -v/3

➠ v = -9 m

∴ Mirror should be placed at a distance of 9m from the lamp in order to get clear image.

Note : Negative sign indicates that image is inverted.

Applying mirror formula :-

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

$:\implies\sf\:\dfrac{1}{(-3)}+\dfrac{1}{(-9)}=\dfrac{1}{f}$

$:\implies\sf\:\dfrac{-3-1}{9}=\dfrac{1}{f}$

$:\implies\sf\:\dfrac{-4}{9}=\dfrac{1}{f}$

$:\implies\sf\:f=\dfrac{(-9)}{4}$

$:\implies\:\underline{\boxed{\bf{\purple{f=-2.25\:m}}}}$

Answer 2

Answer:

Given

• height of the flame = 0.03 m
• distance of the object = 3 m
• mirror: concave
• magnification= 3

To Find

1. Distance of image and focal
2. Focal length of the image

Solution

First find distance of image in order to find focal length of the mirror.

Formula for the magnification of the mirror:

▪️m= -v/u

substituting the value in the above formula

$3 = \frac{ - v}{3} \\ \to \: v = - 9m$

∴ Mirror has to be placed at a distance of 9m from the lamp in order to get clear image.

$\bold \red{Mirror \: Formula}$

$\bold{ \frac{1}{v} + \frac{1}{u} = \frac{1}{f} }$

▪️substitute the values in the formula to find the focal length of the mirror-

$\bold{➠\frac{1}{ - 3} + \frac{1}{ - 9} = \frac{1}{f} }$

$\bold{➠ \frac{ - 3 - 1}{9} = \frac{1}{f} } \\ \\ ➠ \bold{ \frac{ - 4}{9} = \frac{1}{f} } \\ \\ ➠\bold \green{ f = - 2.25 \: metre}$