Question

A point source with luminous intensity I₀ = 100 cd is positioned at a distance s = 20.0 cm from the crest of a concave mirror with focal length f = 25.0 cm. Find the luminous intensity of the reflected ray if the reflection coefficient of the mirror is ρ = 0.80.

Answer 1

For a concave mirror as usual 

(In coordinate convention s = - s is negative & f = -|f| is also negative.) 

If A is the area of the mirror (assumed small) and the object is on the principal axis, then the light incident on the mirror per second is 

This follows from the definition of luminous intensity as light emitted per second per unit solid angle in a given direction and the fact that A/s² is the solid angle subtended by the mirror at the source. of this a fraction ρ is reflected so if I is the luminous intensity of the image,

(Because our convention makes f - ve for a concave mirror, we have to write |f|.) 

Substitution gives    I = 2.0 x 10³ cd.