Answer to Question #205112 in Optics for anuj

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

$\text{Lens Formula:}$

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

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

$v=\frac{u*f}{u-f};$

$f=200mm =0.2m$

$u=10km=10000m$

$v=\frac{10000*0.2}{10000-0.2}\approx0.2m$

$\text{Answer : (a) Where is the image? 0.2 m}$

$\text{Magnification:}$

$m=\frac{\text{Heigh of Image}}{\text{Heigh of Object}}; ​$

$m=\frac{v}{u}$

$\text{Heigh of Image}={\text{Heigh of Object}}*\frac{v}{u}$

${\text{Heigh of Object}}=1000m$

$\text{Heigh of Image}=1000*\frac{0.2}{10000}=0.02m$

$\text{Answer: }$

$\text{What is the height of the image of a 1000 m high cliff on one of the mountains? 0.02m}$