Question

A 12m tall tree is to be photographed with a pin hole camera. It is situated 15m away from the pin hole. How far should the screen be placed from the pin hole to obtain a 12cm tall image of a tree?

Answer 1

See the attachment......!!!!

Answer 2

Formula we will be using:
[tex]\text{ (i) Magnification}= \frac{H_i}{H_o}= \frac{D_i}{D_o} \text{ where} \\ H_o=\text{height of the object}  \\ H_i=\text{Height of the image} \\ D_o=\text{Distance of the object} \\ D_i=\text{Distance of the image} [/tex]
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Given,
[tex]H_o=\text{height of the object} =\text{ height of the tree = 12m=1200cm} \\ H_i=\text{Height of the image} =\text{ height of the image of the tree = 12cm} \\ [/tex]
[tex]D_o=\text{Distance of the object } \\ =\text{Distance of the tree from the pinhole.}=15m=1500cm\\ D_i=\text{Distance of the image = Distance of the image from the pinhole.}\\ [/tex]

Plug in the known values in the formula:


$\text{ Magnification}= \frac{H_i}{H_o}= \frac{D_i}{D_o} \\ \frac{H_i}{H_o}= \frac{D_i}{D_o} \\ \frac{12}{1200}= \frac{D_i}{1500} \\ \text { Multiply both sides by 1500}: \\ \frac{12}{1200}*1500= D_i \\ D_i=15$

Distance of the image = 15cm

Therefore, the screen should be placed 15cm from the pinhole.

Answer : 15cm