Question

A $2.0\mathrm{m}$tall man is $10\mathrm{m}$in front of a camera with a $15\mathrm{mm}$focal length lens. How tall is his image on the detector?

Short answer

The height of the image will be$0.0015\mathrm{m}.$

Step-by-step solution

Given information

We have given,

Height of the man = $2\mathrm{m}$

Distance from the camera = $10\mathrm{m}$

focal length of the camera = $15\mathrm{mm}=0.015\mathrm{m}$

We have to find the height of the image.

Simplify

Since the camera uses a converging lens.

then using the lens's equation

$$\begin{gathered} \frac{1}{\mathrm{f}}=\frac{1}{v}-\frac{1}{u} \\ \frac{1}{0.015}=\frac{1}{v}-\frac{1}{-10} \\ \frac{1}{v}=\frac{1}{0.015}-\frac{1}{10}=\frac{9.985}{0.15} \\ v=0.015m \end{gathered}$$

Since the image formed by the lens is inverted.

$$\begin{gathered} m=\frac{Heightoftheimage}{Heightoftheobject}=\frac{h\text{'}}{h} \\ \frac{h\text{'}}{2}=\frac{v}{u}=\frac{0.015}{10} \\ h\text{'}=-0.0015m \end{gathered}$$