A point source with luminous intensity `I_(0) = 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 `rho = 0.80`.

Explanation

For a convace mirror as usual `(1)/(s') + (1)/(s) = (1)/(f)` so `s' = (s f)/(s - f)`
(In corrdiante convention `s =-s` is negative & `f =-|f|` is also negative.)
If `A` is the area of the mirror (assumed small) an dthe object is on the principle axis, then the light incident on the mirror per second is `I_(0) (A)/(s^(2))`.
This follows from the defination of luminous intensity as light emitted per second per unit solid angle in a given direction and the fact that `(A)/(s^(2))` is the solid subtenden by the mirror at the source. Of this a fraction `rho` is refected so if `I` is the luminous intensity of the image, then `I (A)/(s'^(2)) = rho I_(0) (A)/(s^(2))`
Hence `I = rho I_(0) ((|f|)/(|f|-s))^(2)`
(Beacuse our convention makes `f - ve` for a concave mirror, we hwve to write `|f|`.)
Substitution gives `I = 2.0 xx 10^(3) cd`.