Use the mirror equation to deduce that:

(a) An object placed between f and 2f of a concave mirror produces a real image beyond 2f.

(b) A convex mirror always produces a virtual image independent of the location of the object.

(c) The virtual image produced by a convex mirror is always diminished in size and is located between the focus and the pole.

(d) An object placed between the pole and focus of a concave mirror produces a virtual and enlarged image.

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(a) The image lies beyond 2f, (b) A convex mirror always produces a virtual image, regardless of the object distance, (c) The image formed is diminished and is located between the focus (f) and the pole, (d) The formed image is enlarged.

(a) The image lies beyond f, (b) A convex mirror always produces a virtual image, regardless of the object distance, (c) The image formed is diminished and is located between the focus (f) and the pole, (d) The formed image is enlarged.

(a) The image lies beyond 2f, (b) A convex mirror always produces a virtual image, regardless of the object distance, (c) The image formed is diminished and is located between the pole, (d) The formed image is enlarged.

None of these

answer is A.

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Detailed Solution

Concept: This question is the easy application of the mirror formula. You have to use right sign convention and put the values (that are given to you in the question) in the mirror formula. After that, find the relation between u, v, and f to answer each part. Also solve the question part by part.
a) For a concave mirror, the focal length (f) is negative.
When the object is placed on the left side of the mirror, the object distance (u) is negative
For image distance

we can write

The object lies between

and 2 f.

from eq. 1

is negative

Therefore, the image lies beyond

.
b) For a convex mirror, the focal length (f) is positive
When the object is placed on the left side of the mirror, the object distance (u) is negative
For image distance v, we have the mirror formula

Using eq (2)

Thus, the image is formed on the back side of the mirror.
Hence, a convex mirror always produces a virtual image, regardless of the object distance.
c) For a convex mirror, the focal length (f) is positive When the object is placed on the left side of the mirror, the object distance (u) is negative For image distance

, we have the mirror formula

but

therefore

Hence, the image formed is diminished and is located between the focus (f) and the pole
d) For a concave mirror, the focal length (f) is negative
When the object is placed on the left side of the mirror, the object distance (u) is negative
It is placed between the focus (f) and the pole therefore

For image distance

, we have the mirror formula

The image is formed on the right side of the mirror. Hence, it is a virtual image For

and

, we can write:

magnification

So, the formed image is enlarged.
Hence, option 1 is correct.

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