Question

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

• A. $\frac{\left(f\right)}{f+p}$
• B. $\frac{f}{p}$
• C. $\sqrt{\frac{f}{p}}$
• D. $\frac{f^2}{p^2}$

Answer 1

The correct option is A $\frac{\left(f\right)}{f+p}$

$\begin{array}{c}\text{Focal length}=f\\ \text{distance of object}-P=u\\ \text{To find}\Rightarrow \frac{I}{0}\end{array}$

$\begin{array}{c}I=\text{size of image}\\ O=\text{size of object}\end{array}$

$\begin{array}{c}\text{magnification}=m=\frac{I}{O}=-\frac{v}{u}-\left(i\right)\\ \text{Mirror formula;}\\ \frac{1}{v}-\frac{1}{u}=\frac{1}{f}\\ \frac{1}{v}-\frac{1}{p}=\frac{1}{f}\\ \frac{1}{v}=\frac{1}{f}+\frac{1}{p}\\ \frac{1}{v}=\frac{p+5}{pf}\\ v=\frac{pf}{p+f}\end{array}$

$\begin{array}{cc}\text{Putting in}& \text{(i)}\\ \begin{array}{cc}\frac{I}{O}& =-\frac{pf}{(P+f)\times P}\\ & =-\frac{f}{P+f}\\ & =\frac{f}{P+f}\end{array}& \end{array}$