Answer to Question #126474 in Mechanics | Relativity for Stefanie Hernandez-Mendez

Question

Suppose a 200-mm focal length telephoto lens is being used to photograph mountains 12.5 km away.
What is image distance, in meters, for this lens?
What is the image height, in centimeters, of a 950-m high cliff on one of the mountains?

Answer 1

The lens formula is used to obtain the image distance

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

$\frac{1}{v}=\frac{1}{f}-\frac{1}{u}$

$\frac{1}{v}=\frac{ 1}{0.2}-\frac{1}{12500}$

$v= 0.2 meters$

image distance= 0.2m

To get the image height , magnification should first be calculated

$m=\frac{imagedistance}{object distance}$

$m=\frac{ 0.2}{12500}= 1.6\times10^{-5}$

$m=\frac{ height of image}{heightof object}$

$heightofimage= (1.6\times10^{-5})\times950=0.0152 m$

height of image in cm is 1.52 cm