An object is held 19.5 cm away from a mirror. The mirror has a focal length of -

Question

An object is held 19.5 cm away from a mirror. The mirror has a focal length of -64 cm.

a.) Determine the image distance in cm.

b.) Determine the magnification.

c.) If the object is 0.9 cm long, determine the image height. cm

d.) Which of the following are true about the image? Choose all that apply.
The image is virtual.
The image is inverted.
The image is upright.
The image is real.

e.) Which of the following are true about the mirror? Choose all that apply.
The mirror is convex.
The mirror is diverging.
The mirror is concave.
The mirror is converging.

Explanation / Answer

In this problem, we are given:

The object distance = do = 1.3 cm
Focal length of the mirror = f = -74.8 cm

a) Since we know the relationship:

1/f = 1/do + 1/di

We can use it and solve for di:

1/di = -1/74.8 cm - 1/1.3 cm

di = -1.28 cm

b) We know that magnification = M = -di/do

M = 1.28 cm/1.3 cm

M = .985

c) We have that the height of the object = ho = 0.9 cm

M = hi /ho

0.985 = hi/0.9 cm

We now solve for hi

hi = 0.8865 cm

d) Since image location, di is negative, the image is virtual
and M is positive, therefore, the image is upright

e) Since f is negative, the mirror is a diverging convex mirror

I hope this helps you out! If something is unclear, let me know!

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