As a gift for your birthday you receive a new lens for your 35 mm camera. (We ar

Question

As a gift for your birthday you receive a new lens for your 35 mm camera. (We are presuming that you previously were given a 35 mm camera that uses film because you wanted to get into photography and one of your parents had such a camera around the house. Eventually you will get a digital camera, but for the moment you are happy to settle for film on the non-automatic camera so you can really learn how the camera works, understand light levels, etc.) The lens is a lens that is good for portraits (so you can take pictures of people) and has a focal length of 105 mm. If the object (your niece) is located 4 meters in front of the lens and is 3 feet tall, (a) how far behind the lens is the image and (b) how big is the image that will appear on the film or digital chip? (c) Suppose the object is only 1 meter in front of the lens. In this second case, how far behind the lens is the image? [Part b in this example is the most difficult part, so please expect that.]

Explanation / Answer

1/f = 1/o +1/i

f=10.5 cm

o= -400cm

so ;

use sign convention;hence o is

1/10.5= (-1/400) +(1/i)

=>1/i=0.097738

i=10.23 cm

hence the image is real

b) magnification is given by

(-i/o) = (hi/ho)

=>- (10.23/(400))= (hi/3)

=>hi=-0.0767 feet

=-2.33cm high(negative sign indicates the image is inverted in the chip;

c) 1/10.5= (1/-100) +(1/i)

=>1/i=0.1052

i=9.5022 cm behind the lens

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