Problem 22.42 A camera with an 8.0-cm focal length lens is used to photograph a

Question

Problem 22.42

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.

Part A

Calculate the closest distance the person can stand to the lens.

Express your answer to two significant figures and include the appropriate units.

Part B

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.

Problem 22.42

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.

Part A

Calculate the closest distance the person can stand to the lens.

Express your answer to two significant figures and include the appropriate units.

s =

Part B

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.

s =

Explanation / Answer

let the object distance be -u and image distance be v.

assuming that a concave lens is used , hence we obtain an inverted image.

then object height= 2m

image height=-0.035 m

where u and v , both are positive quantities.

now as we know, image height/object height=image distance/object distance

==> -0.035/2=v/-u

==> u=57.1428*v....(1)

using lens equation:

(1/image distance)-(1/object distance)=1/focal length

we get

(1/v)-(1/-u)=1/0.08

==> (1/v)+(1/(57.1428*v))=1/0.08

==> v=0.0814 m=8.14 cm

==> u=57.1428*v=4.651 m

so the person has to stand at a distance of 4.65 m from the camera.

and the film should be 8.14 cm distance from the lens.

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