When an object is placed at a distance of from a concave spherical mirror, the magnification produced is . The object distance for the image to have a magnification of to be:

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from the mirror to the left

from the mirror to the right

200 cm from the mirror to the left

None of these

answer is A.

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Detailed Solution

Concept- Using a concave mirror with a certain focal length, a magnification of

when placed at

from the mirror. Finding the object distance to obtain the desired magnification requires finding the focal length using the mirror formula

.
We are given a concave mirror with a focal length of "f" that, when an item is placed

cm from its reflecting surface, creates an image with a magnification of "

Using the mirror formula and the magnifying formula for reflecting surfaces, we can quickly determine the focal length.
Question Image

As far as we know, the mirror formula is provided by

Where,

is the focal length of the concave mirror,
The distance between an item and a reflecting surface is indicated by the letters u and v, respectively.
Here,

In order to get the image distance "v," we can now use the formula to obtain the magnification in terms of object distance and image distance.
also,
magnification,

given,

Now we can use them in the mirror formula to obtain the concave mirror's focal length as –

and

Now, let us find the object distance to get an image of magnification

with a focal length of

.
given,

We may now use the mirror formula to get the object's distance, or "u."

We got the object distance for the image to have a magnification of

to be

from the mirror to the left.
Hence, the correct option is 1.

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