Question

The focal length of a concave mirror is f and the distance from the object to the principal focus is p. The ratio of the size of the real image to the size of the object is:

• A. $-\frac{f}{p}$
• B. ${\left(\frac{f}{p}\right)}^2$
• C. ${\left(\frac{f}{p}\right)}^{\frac{1}{2}}$
• D. $-\frac{p}{f}$
• E. $-fp$

Answer 1

The correct option is A $-\frac{f}{p}$

Distance of object is $u=-(f+p)$

$\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$ gives:

$\frac{1}{v}-\frac{1}{f+p}=-\frac{1}{f}$

or, $\frac{1}{v}=-\frac{1}{f}+\frac{1}{f+p}$

or, $\frac{1}{v}=-\frac{p}{(f+p)\times f}$

or, $v=-\frac{(f+p)\times f}{p}$ (-ve sign indicates image is real)

Magnification $=-\frac{v}{u}$

$=-\frac{(f+p)\times f}{p\times (f+p)}$

$=-\frac{f}{p}$ (-ve sign indicates inverted)

So, ratio of size of image to that of object is: $-\frac{f}{p}$