55.  A tourist takes a picture of a mountain 14 km away using a camera that has a lens with a focal length of 50 mm. She then takes a second picture when she is only 5.0 km away. What is the ratio of the height of the mountain’s image on the camera’s image sensor for the second picture to its height on the image sensor for the first picture?

 

the lens equation tells us

Solve for image distance

Magnification gives us

Solving for height of image

 

Similarly

So the ratio is

Because the focal length is so small compared to the object distances, the image distances are essentially the focal length of the lens and so

 

So

 

 

Below, I show that the image distances are essentially the same and therefore if you did the problem this way you would a get a ratio of 1 which is wrong!

 

 

 

 

Magnification gives us

Solve for image height

 

 

 

 

Magnification gives us

Solve for image height

 

 

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This page last updated on July 6, 2018