Question

Between which two points of the concave mirror should an object be placed to obtain a magnification of:
(a) -3 (b) +2.5 (c) -0.4

Answer 1

Hint: The magnification of the mirror is the size of the image by the size of the object. The magnification can also be defined as the distance of the image by the distance of the object. Using the properties of the magnification of the concave mirror we will be solving the problem.
Formula used:
$$\begin{array}{rl}& m=-{\displaystyle \frac{v}{u}}\\ & m={\displaystyle \frac{v}{-u}}\end{array}$$

Complete answer:
From the given information, we have the data as follows.
The magnification of a spherical mirror is the ratio of the size of the image formed by the mirror to the size of the object.
In the case of the concave mirror, when the image formed is real, the magnification will be negative. Similarly, when the image formed is virtual, the magnification will be positive. If the magnification is negative, the image formed will be real, inverted and enlarged.
For the magnification value of -3, the image formed will be real, inverted and enlarged/magnified. The object must be placed between the principal focus F and the centre of curvature C of the concave mirror.
The ray diagram representing the object placed between the principal focus F and the centre of curvature C of the concave mirror.

For the magnification value of +2.5, the image formed will be virtual and erect. The object must be placed between the pole and the principal focus (F) of the concave mirror.
The ray diagram representing the object placed between the pole and the principal focus (F) of the concave mirror.

For the magnification value of -0.4, the image formed will be real, inverted and diminished. The object must be placed beyond the centre of curvature C of the concave mirror.
The ray diagram representing the object placed beyond the centre of curvature C of the concave mirror.

The mirror table of the concave mirror.

Object location	Large or small	Virtual or real	Inverted or erect	Position
Beyond 2F	Small	Real	Inverted	Between F and 2F
At 2F	Same	Real	Inverted	At 2F
Between 2F and F	Large	Real	Inverted	Beyond 2F
Between F and the lens	Large	Virtual	Erect	Behind the mirror

$$\therefore$$ The magnification of: (a) -3, the object should be placed between the principal focus F and the centre of curvature C (b) +2.5, the object should be placed between the pole and the principal focus (F) (c) -0.4, the object should be placed beyond the centre of curvature.
Note:
The magnification is also called linear magnification. In the case of a convex mirror, the magnification will be positive.