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The image of an object formed by a mirror is real, inverted and the magnification is $- 1 .$ When, the image is at a distance of $40 cm$ from the mirror, if the object is moved $20 cm$ towards the mirror image would be formed:

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Beyond C

Between C and f

At infinity

Behind the mirror

answer is C.

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Detailed Solution

The image of an object formed by a mirror is real, inverted and is of magnification

- 1 .

The image is at a distance of

40 cm

from the mirror, if the object is moved

20 cm

towards the mirror image would be at infinity.
It has been given that,
Magnification,

m = - 1

Image distance,

v = - 40 cm

Now,

m = \frac{- v}{u}

\Rightarrow - 1 = \frac{- (- 40)}{u}

u = - 40 cm

So, object and image both are in the same position. Therefore this point must be the center of curvature.
Now, since the magnitude of

f

is half of the center of curvature,

\Rightarrow f = \frac{40}{2}

f = 20 cm

Now, if the object is moved

20 cm

towards the mirror then its new position would be at the focus of the mirror.
Object distance,

(u) = - 20 cm

Focal length

(f) = - 20 cm

We know that when an object is kept at the focus of a concave mirror, the image is formed at infinity.

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