Question #126474

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?

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?

Expert's answer

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**

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