Question

The figure shown initial position of a source of light $S$ and a light detector $D$. Both $S$ & $D$ move with velocity $10cm/s$, as shown .The converging lens of focal length $20cm$ is fixed. Time instant $\left(s\right)$ when the detector detects maximum intensity of light is / are:-

• A. $3sec$
• B. $4.5sec$
• C. $6sec$
• D. equal intensity at all time

Answer 1

The correct option is A $3sec$

$\begin{array}{c}\text{Let the time instant be}t\text{.}\\ \text{distance travelled by}s=10t\\ \text{Distance travelled by}D=\text{image distance}=10t\\ \text{object distance}=90-10t\\ \text{focal length}=20cm\\ \text{lens formula}\\ \begin{array}{c}\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\\ \frac{1}{20}=\frac{1}{10t}-\frac{1}{-(90-10t)}\end{array}\end{array}$

$\begin{array}{cc}& \begin{array}{c}\frac{1}{20}=\frac{1}{10t}+\frac{1}{90-10t}\\ 20=\frac{10t(90-10t)}{90}\\ 180=t(90-10t)\\ 18=t(9-t)\\ t=3\sec \end{array}\\ & \text{So option}A\text{is correct}\end{array}$