Question

Srikar focussed separately on two objects of different sizes using a photographic camera. He found that the sizes of the images of the two objects, one is kept at a distance of $200m$ and the other at a distance of $2m$ is the same. How did he achieve this? Explain.

Answer 1

Step 1: Compute the magnification of objects.

The image sizes of both objects are the same $v_1=v_2=v$.

The magnification of the first object is,

$$\begin{gathered} m_1=\frac{h_i}{h_{o1}}=\frac{v}{u_1} \\ \Rightarrow \frac{h_i}{h_{o1}}=\frac{v}{200}......\left(1\right) \end{gathered}$$

The magnification of the second object is,

$$\begin{gathered} m_2=\frac{h_i}{h_{o2}}=\frac{v}{u_2} \\ \Rightarrow \frac{h_i}{h_{o2}}=\frac{v}{2}......\left(2\right) \end{gathered}$$

Step 2: Compute the height of objects.

Divide the equations.

$$\begin{gathered} \frac{h_i}{h_{o1}}\times \frac{h_{o2}}{h_i}=\frac{v}{200}\times \frac{2}{v} \\ \Rightarrow \frac{h_{o2}}{h_{o1}}=\frac{1}{100} \\ \therefore h_{o1}=100h_{o2} \end{gathered}$$

From the above equation, it is clear that the height of the first object is$100$ times more than the height of the second object.

Therefore, using the different sized objects, Srikar obtained the same image height of objects placed at different positions.