Question

The distance between an object and a screen is $100cm$. A lens produces an image on the screen when the lens is placed at either of the positions $40cm$ apart. What will be the power of lens, approximately?

Answer 1

Step 1: Given

Distance between object and screen: $D=100cm=1m$

Distance between the two positions of lens: $d=40cm=0.4m$

Step 2: Formula Used

$f=\frac{D^2-d^2}{4D}$

$P=\frac{1}{f}$

Step 3: Find the focal length of the lens

Use the formula for focal length in displacement method

$\begin{array}{rcl}f& =& \frac{{\left(1m\right)}^2-{\left(0.4m\right)}^2}{4\left(1m\right)}\\ & =& \frac{1-0.16}{4}m\\ & =& \frac{0.84}{4}m\\ & =& 0.21m\end{array}$

Step 4: Calculate the power of the lens

$\begin{array}{rcl}P& =& \frac{1}{0.21m}\\ & =& 4.76diopter\\ & \approx & 5diopter\end{array}$

Hence, the power of the lens is $\begin{array}{rcl}& & 5diopter\end{array}$.