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

(a) To obtain a magnification of $-$3

An object should be placed in front of a concave mirror, between the centre of curvature $(C)$ and focus $(F)$ to obtain a magnification of $-$3.

Explanation

Given:

Magnification, $m$ = $-$3

Here, magnification is with the negative sign $(-)$, which implies that the image is real and inverted.

$\because m>1\Rightarrow $ the size of the image is greater than that of the object.

In the case of the concave mirror, both of the above-mentioned conditions are only possible when the object is placed between the centre of curvature $(C)$ and focus $(F)$ in front of the mirror.

(b) To obtain a magnification of $+$2.5

An object should be placed in front of a concave mirror, between the focus $(F)$ and the pole $(P)$ to obtain a magnification of +2.5.

Explanation

Given:

Magnification, $m$ = $+$2.5

Here, magnification is with the positive sign $(+)$, which implies that the image is virtual and erect.

$\because m>1\Rightarrow $ the size of the image is greater than that of the object.

In the case of the concave mirror, both of the above-mentioned conditions are only possible when the object is placed between the focus $(F)$ and the pole $(P)$ in front of the mirror.

(c) To obtain a magnification of $-$0.4

An object should be placed in front of a concave mirror, beyond the centre of curvature $(C)$ to obtain a magnification of $-$0.4.

Explanation

Given:

Magnification, $m$ = $-$0.4

Here, magnification is with the positive sign $(-)$, which implies that the image is real and inverted.

$\because m<1\Rightarrow $ the size of the image is much smaller than that of the object.

In the case of the concave mirror, both of the above-mentioned conditions are only possible when the object is placed beyond the centre of curvature $(C)$ in front of the mirror.