Question
Thu November 17, 2011 By:

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

Expert Reply
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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