The radius of curvature of a concave mirror is given by R = 2 f . A plane mirror

Question

1. The radius of curvature of a concave mirror is given by R = 2f. A plane mirror essentially has an infinite radius of curvature. Using this conjecture, verify that, regardless of the object distance, the image of an object formed by a plane mirror is (a) always virtual, (b) is always the same distance behind the mirror as the object is in front of the mirror, and (c) that the image always has a magnification of m = +1. Show all of your work. (Note: By convention, an image is virtual instead of real if the image distance is negative. For a mirror, this would put the image behind the mirror as is the case for a plane mirror.)

Explanation / Answer

a)
for a plane mirro, R = infinite

f = R/2 = infinite

let u is the object distnce and v is image distance

1/u + 1/v = 1/f

1/u + 1/v = 1/infinite

1/u + 1/v = 0

==> 1/u = -1/v

==> v = -u

- sign indicates the image is virtual

b) |v| = |u|

c) m = -v/u = -(-u/u) = 1

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