Spherical mirror formula relating an object distance 'u', image distance 'v' and focal length of mirror 'f' may be applied to a plane mirror when
- A.focal length goes to infinity.
- B.focal length goes to zero.
- C.image distance goes to zero.
- D.image distance goes to infinity.
Correct answer
Explanation
The correct answer is A, focal length goes to infinity. A plane mirror is a spherical mirror of infinite radius of curvature, so its focal length f = R/2 is also infinite.
The mirror formula is 1/v + 1/u = 1/f. When f becomes infinitely large, 1/f becomes zero, so 1/v = −1/u and v = −u. In the sign convention this means the image is as far behind the mirror as the object is in front of it, which is exactly what a plane mirror does. The magnification m = −v/u then becomes +1: the image is virtual, erect and of the same size as the object. A plane mirror can thus be treated as the limiting case of a very flat curved mirror.
B is wrong because a focal length near zero would mean an extremely curved mirror, the opposite of a flat one. C is wrong because an image distance of zero would put the image on the mirror surface, which a plane mirror does not do. D is wrong because the image goes to infinity only when the object is at the focus of a concave mirror.
Exam tip: Plane mirror – R and f infinite, v = −u, magnification +1.
Practice Questions
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