1.

Derive the relation f = R//2 in the case of a concave mirror.

Answer»

Solution :
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 refraction, the ray AB passes along BD,through the focus F. BC is NORMAL to the concave mirror at B.
`/_ABC = /_ CBD `.....(1)
( According to the law of reflection ` /_i= /_ r )`
We know that AB and PC are parallel to each other.
`:. /_ ABC = /_ BCP ` ( alternate ANGLES )....... (2)
From equations (1)and (2) , we get
`/_ CBD = /- BCP `
Hence triangleBCF is isosceles
`:. BF = CF`....(3)
If the aperture of the mirror is small than B will be very close to P.
`:.` BF = PF....(4)
From equation ( 3) and( 4)we CONCLUDE that
`CF = PF = ( 1)/(2) PC `
But by definition PF = f ( focal length )and PC = R ( radius of curvature )
i.e., `f = ( R )/( 2)`


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