Answer to Question #200391 in Optics for Piolo

Question

Suppose a 200 mm-focal length telephoto lens is being used to photograph mountains 10.0 km away.

(a) Where is the image? ______ m

(b) What is the height of the image of a 1000 m high cliff on one of the mountains? ______ m

Answer 1

The lens formula is used to obtain the image distance

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

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

$\frac{1}{v}=\frac{ 1}{0.2}-\frac{1}{10000}$

$v\approx 0.2 \ meters$

image distance= 0.2m

To get the image height , magnification should first be calculated

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

$m=\frac{ 0.2}{10000}= 2\times10^{-5}$

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

$heightofimage= (2\times10^{-5})\times1000=0.02 m$

height of image in cm is 2 cm