Question #200391

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


1
Expert's answer
2021-06-07T09:40:59-0400

The lens formula is used to obtain the image distance


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


1v=1f1u\frac{1}{v}=\frac{1}{f}-\frac{1}{u}


1v=10.2110000\frac{1}{v}=\frac{ 1}{0.2}-\frac{1}{10000}


v0.2 metersv\approx 0.2 \ meters


image distance= 0.2m


To get the image height , magnification should first be calculated


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


m=0.210000=2×105m=\frac{ 0.2}{10000}= 2\times10^{-5}


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


heightofimage=(2×105)×1000=0.02mheightofimage= (2\times10^{-5})\times1000=0.02 m


height of image in cm is 2 cm

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