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# A convex mirror has focal lenght f. A real object at a distance f in front of its pole produce an image at distance:A. 2fB. fC. f/2D. infinite

Arun
25763 Points
one year ago

The image will be a virtual image (behind the mirror) between the pole and the focus.

The position of the image can be calculated from the well-known mirror formula:

1/f = 1/do + 1/di where “do” is the distance of the object from the pole and “di” is the distance of the image from the pole.

You need to be careful with the signs (+ or -) for the distances. Unfortunately there is more than one “sign convention”. What I will use here is the convention that virtual image distances are negative and the focal length of a convex mirror is also negative.

So, the focal length is minusf and the object distance is plusf.

Hence: -1/f = 1/f + 1/di.

Adding -1/f to both sides of the equation gives -2/f = 1/di. Therefore di = -f/2.

So the image is at a distance f/2 behind the mirror.