Question

A concave mirror of focal length 12 cm is placed at a distance of 60 cm from a wall. How far from the wall an

object be placed so that its sharp image formed by the mirror falls on the wall?​

Answer 1

The distance of object from the wall be 45 cm.

A concave mirror of focal length 12 cm is placed at a distance of 60 cm from a wall.

We have to find the distance from the wall of an object to be placed so that its sharp image formed by the mirror falls on the wall.

See the diagram,

Let the distance of the object from the wall be x.

∴ object distance from the mirror, u = -(60 - x) cm

Here, focal length, f = -12cm

image distance from the mirror, v = - 60cm

Using formula, 1/v + 1/u = 1/f

⇒ 1/-60 + 1/-(60 - x) = 1/-12

⇒ 1/(60 - x) = 1/12 - 1/60 = (5 - 1)/60

⇒ 1/(60 - x) = 1/15  

⇒ x = 45 cm

Therefore the distance of object from the wall be 45 cm.

Answer 2

Step 1: Given data

focal length, $f=12cm$

distance of mirror from the wall $=60cm$

object distance, $u=?$

Step 2: Calculating the object distance

Let,

distance of the object from the wall $=x$

$\therefore$ object distance from the mirror, $u = -(60 - x) cm$

Since, it is a concave mirror,

$f=-12cm$

Since, the image formed is sharp,

image distance, $v=-60cm$

Using the mirror formula,

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

$\frac{1}{-12}=\frac{1}{-60}+\frac{1}{-(60-x)}$

$\frac{1}{60-x} =\frac{1}{12} -\frac{1}{60}$

$\frac{1}{60-x} = \frac{5-1}{60}$

$\frac{1}{60-x} = \frac{1}{15}$

$60-x=15$

$x=60-15=45cm$

Hence, the distance of the object from the wall is $45cm$.

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