Question

A POINT OBJECT IS PLACED ON THE AXIS OF CONCAVE MIRROR AT A DISTANCE OF 60 CM FROM THE FOCAL POINT OF THE MIRROR .IT IMAGE IS FORMED AT THE POINT OF OBJECT . THEN FIND FOCAL LENGTH OF MIRROR.​

Answer 1

Answer:

120 cm

Explanation:

60cm = focal point of object

60cm= focal point of image formed

60+60=120cm (by law of reflection)

Answer 2

Step-by-Step Explanation:

We know that,

$\frac{1}{v}+\frac{1}{u}= \frac{1}{f}$ (Mirror formula)

Where,

$v$ ⇒ Image distance`

$u$ ⇒  Object distance

$f$ ⇒  Focal length

Since both the object and image formed in front of the mirror, at the same place, then,

∴ $u=v = -60$

$\frac{1}{-60}+\frac{1}{-60}= \frac{1}{f}$

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

$-\frac{2}{60}= \frac{1}{f}$

$f= -\frac{60}{2}$

$f=-30$

Therefore, the focal length of the concave mirror is -30cm.

Alternative method:-

Since both the object and image formed in front of the mirror, at the same place, then the object must be placed at the center of curvature.

∴ R = 2f

60 =2f

f = 60/2

f= -30 cm ( -ve sign is given because the focal length of a concave mirror is always negative)

Therefore, the focal length of the concave mirror is -30cm.

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