A camera with an 8.0-cm focal length lens is used to photograph a person who is

Question

A camera with an 8.0-cm focal length lens is used to photograph a person who is 2.0 m tall. The height of the image on the film must be no greater than 3.5 cm. Calculate the closest distance the person can stand to the lens. Express your answer to two significant figures and include the appropriate units. All attempts used; correct answer displayed Not quite. Check through your calculations: you may have made a rounding error or used the wrong number of significant figures. For this object distance, how far should the film be located from the lens? Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

1/f = 1/u + 1/v

===> 1/v = 1/f - 1/u

1/v = (u - f)/uf

v = uf/(u - f)

Magnification = image height / object height = hi/ho

Also

Magnification = image distance / object distance = v/u

hi/ho = 3.5 cm / 200 cm = 3.5/200

3.5/200 = v/u

But v = uf/(u - f)

3.5/200 = {uf/(u - f)}/u

3.5/200 = {f/(u - f)}

3.5/200 = 8/(u - 8)

3.5(u - 8) = 8 x 200

3.5u - 28 = 1600

3.5u = 1600 + 28

3.5u = 1628

u = 465.14 cm

u = 4.6514 m

u = 4.65 m        (3 significant figures)

Part B

u = 4.65 m

f = 8 cm = 0.08 m

1/f = 1/u + 1/v

1/v = 1/f - 1/u

v = uf/(u - f)

v = (4.65 x 0.08)/(4.65 - 0.08)

v = 0.372/4.57

v = 0.0814 m

v = 8.14 x 10-2 m

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