KAPLAN Mirror Qbank problem

[PrinceAli2786]

A light bulb is 10 cm in front of a convex mirror with a focal length of 20 cm. At what distance from the object does the image form?
5.0 cm
6.6 cm
10.0 cm
16.7 cm

[Show/hide explanation]

D

Something that is concave 'ecaves' in, so the convex mirror bulges out towards the light bulb - and that makes it a diverging mirror. Consequently, the focal length is negative. Apply the lens-maker's equation to determine the image distance from the mirror:

The image is formed behind the mirror. You aren't done yet, because the question asks for the distance between object and image. That distance is , answer choice (D).



*I don't get why you don't do 20/3 - 10 = 20/3 - 30/3 = -10/3
isn't that what you do to get the difference in lenghts, subtract? why do they add?

thanks for the help

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[nfg05]

1/f = 1/o + 1/i

f = -20 (the focal length of a convex mirror is negative, the focal length of a concave mirror is positive)
o = 10 (object distances are always positive in single mirror/lens systems)
i = ?

-1/20 = 1/10 + 1/i
1/i = -1/20 - 2/20 = -3/20
i = -20/3 = -6.67

Negative image distance for a mirror means behind the mirror, so the image is 6.67 cm behind the mirror. But they want the distance from the object which is 10 cm in front of the mirror. That's why the answer is 16.67 cm.

Really bad diagram:
o _ _ _ _ 10 _ _ _ _ ( _ _ 6.67 _ _ i

 

[PrinceAli2786]

1/f = 1/o + 1/i

f = -20 (the focal length of a convex mirror is negative, the focal length of a concave mirror is positive)
o = 10 (object distances are always positive in single mirror/lens systems)
i = ?

-1/20 = 1/10 + 1/i
1/i = -1/20 - 2/20 = -3/20
i = -20/3 = -6.67

Negative image distance for a mirror means behind the mirror, so the image is 6.67 cm behind the mirror. But they want the distance from the object which is 10 cm in front of the mirror. That's why the answer is 16.67 cm.

Really bad diagram:
o _ _ _ _ 10 _ _ _ _ ( _ _ 6.67 _ _ i

k I get it now! Thanks, I missed the part that it says the answer we get is in relation to the mirror