An object is held 62.3 cm away from a lens. The lens has a focal length of 90 cm

Question

An object is held 62.3 cm away from a lens. The lens has a focal length of 90 cm.

a.) Determine the image distance.
1______________ cm

b.) Determine the magnification.
2______________

c.) If the object is 9.3 cm long, determine the image height.
3______________cm

d.) Which of the following are true about the image? Choose all that apply.

e.) Which of the following are true about the lens? Choose all that apply.

The lens is convex.

The lens is diverging.

The lens is concave.

The lens is converging.

Explanation / Answer

Use the lens equation

1/f = 1/do + 1/di
with f = 90 cm
do = 62.3 cm

then
1/(90cm) = 1/(62.3cm) + 1/di
1/di = 1/(90cm) - 1/(62.3cm)
1/di = -4.940 cm-1

di = -202.4 cm

a) the image distance is -202 cm

magnification is

m=-do/di

m=-(-202cm)/(62.3cm)

m = +3.25

b)the magnification is +3.25

the object height is 9.3 cm long

c) the image height is (3.25)(9.3cm) = 30.2 cm

d) the image is virtual because di is negative, the image is upright because m is positive

e) the lens is convex, the lens is converging

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