A lamp mainly emits light of wavelength `lambda`. The lamp is rated at P watt and 8% of the energy is emitted as visible light.
(i) How many photons of light are emitted by the lamp per second?
(ii) How many photons are falling per second on a square whose length of each side is a, held perpendicular to the incident photons at a distance r from the lamp.

Explanation

(i) Energy of each photon, `E=(hc)/lambda`
Light energy emitted per second by lamp
`8/100P`
No. of photons of light emitted by lamp per second,
`N=(8P//100)/(hc//lambda)=(8Plambda)/(100hc)`
(ii) No. of phtons falling per second on square
`=N/(4pir^2)xxa^2=(8Plambda)/(100hc)xx(a^2)/(4pir^2)=1/50 (Plambdaa^2)/(pihcr^2)`