# Physics Class 12 NCERT Solutions: Chapter 9 Ray Optics and Optical Instruments Part 7

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Q: 15. Use the mirror equation to deduce that:

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

(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.

[Note: This exercise helps you deduce algebraically properties of images that one obtains from explicit ray diagrams.]

Answer:

(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 v, we can write the lens formula as:

The object lies between and.

( and f are negative)

Using equation (1), we get:

is negative, i.e., 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 equation (2), we can conclude that:

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 v, we have the mirror formula:

But we have

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.

For image distance v, 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,

Hence, the formed image is enlarged.