1.) A real object and its real inverted image are to be 4.4 m apart. There are t

Question

1.) A real object and its real inverted image are to be 4.4 m apart. There are two possible locations for the lens relative to the position of the object.
What is the location of the object when the image is twice the size of the object?

What is the other possible location? (When the image is NOT twice the size of the object.)

What is the focal length of the lens?

2.)An object is 16.9 cm to the left of a thin diverging lens having a -34.1 cm focal length.
What is the image distance?

3.)A movie camera with a (single) lens of focal length 50.0 mm takes a picture of a person standing 23.7 m away. If the person is 180 cm tall, what is the height of the image on the film?

Explanation / Answer

1) Given: do + di = 4.4

For hi = -2ho :

hi / ho = -di / do

=> -2 = -di / do

=> di = 2do

Using the firsr equation, we get,

do + 2do = 4.4

=> do = 1.5 m

Also, 1/do + 1/di = 1/f

=> f = dodi / (do + di) = 1.5 * (4.4 - 1.5) / 4.4 = 1 m

For the other location:

1/do + 1/(4.4 - do) = 1/1

=> do(4.4 - do) = 4.4

=> do2 - 4.4do + 4.4 = 0

Sum of roots: do + 1.5 = 4.4

=> do = 2.9 m (other possible location)

2) 1/16.9 + 1/di = 1/(-34.1)

=> di = -34.1 * 16.9 / (34.1 + 16.9) = -11.3 cm

3) di = fdo/(do - f) = 5 * 2370 / (2370 - 5) = 5 cm

hi = -(di/do)ho = -(5 / 2370) * 180 = 0.4 cm

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