Question

When an object is kept at a distance of $30cm$ from a concave mirror, the image is formed at a distance of $10cm$. If the object is moved with a speed of $9cm{s}^{-1}$ the speed with which the image moves is

• A. $0.1cm{s}^{-1}$
• B. $1cm{s}^{-1}$
• C. $3cm{s}^{-1}$
• D. $9cm{s}^{-1}$

Answer 1

Answer: (B)

$1cm{s}^{-1}$

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

$-\frac{du}{u^2}-\frac{dv}{v^2}=0$ or $-\frac{dv}{v^2}-\frac{du}{u^2}$

or $dv=-\frac{v^2}{u^2}du$

$=-\frac{10\times 10}{30\times 30}\times 9cm{s}^{-1}=-1cm{s}^{-1}$.