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Question
Thu November 17, 2011 By:

# 1.prove that R=2F for a concave or convex mirror.

Fri November 18, 2011
For Concave Mirror

To Show that f = R/2 for a Concave Mirror

Let a ray of light AB be incident, parallel to the principal axis, on a concave mirror. After reflection, the ray AB passes along BD, through the focus F. BC is normal to the concave mirror at B.

We know that AB and PC are parallel to each other.

From equations (1) and (2) we get

Hence triangle BCF is isosceles

BF = CF --------- (3)

If the aperture of the mirror is small then B will be very close to P.

BF = PF --------- (4)

From equations (3) and (4) we conclude that

But by definition PF = f (focal length) and PC = R (radius of curvature)

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