Question

The real image of an extended object, placed in front of a concave mirror, is formed at a distance of 40 cm from the object. If the image is 3 times bigger than the object, the magnitude of focal length of the mirror is ?

• A. 15 cm
• B. 10 cm
• C. 20 cm
• D. 5 cm

Answer 1

The correct option is A 15 cm

Given,

$\begin{array}{c}\text{Distance. between object and image}=40\\ \text{and}\begin{array}{c}\frac{h_i}{h_m}=-3=\text{magnification}\\ -\frac{v}{u}=-3\end{array}\\ \text{for a real object if the magnification}\\ \text{is greater than one then its means}\\ \text{that the object is between Radius}\\ \text{of curvature point and focus.}\\ \text{Inverted image is formed in between}\\ \text{infinity and radius of curvature point}\end{array}$

by Given

$-\frac{v}{u}=-3\Rightarrow [v=3u]-\left(1\right)$

$v-u=40$

$3u-u=40by\left(1\right)$

$\sqrt{u}=20cmv=3u=60cm$

formula

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

$\begin{array}{cc}\frac{1}{f}& =\frac{1}{-60}+\frac{1}{-20}\\ f& =-\frac{60}{4}\\ f& =-15cm\end{array}$

so focal tength of mirror = $15cm$

Option $A$ is correct.