The filament of a light bulb has surface area

PHYSICS · Single correct · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

64\text{ mm}^2

. The filament can be considered as a black body at temperature

2500\text{ K}

emitting radiation like a point source when viewed from far. At night the light bulb is observed from a distance of

100\text{ m}

. Assume the pupil of the eyes of the observer to be circular with radius

3\text{ mm}

. Then (Take Stefan-Boltzmann constant

= 5.67 \times 10^{-8}\text{ Wm}^{-2}\text{K}^{-4}

, Wien's displacement constant

= 2.90 \times 10^{-3}\text{ m}\cdot\text{K}

, Planck's constant

= 6.63 \times 10^{-34}\text{ Js}

, speed of light in vacuum

= 3.00 \times 10^8\text{ ms}^{-1}

) (1) power radiated by the filament is in the range

642\text{ W}

645\text{ W}

(2) radiated power entering into one eye of the observer is in the range

3.15 \times 10^{-8}\text{ W}

3.25 \times 10^{-8}\text{ W}

(3) the wavelength corresponding to the maximum intensity of light is

1160\text{ nm}

(4) taking the average wavelength of emitted radiation to be

1740\text{ nm}

, the total number of photons entering per second into one eye of the observer is in the range

2.75 \times 10^{11}

2.85 \times 10^{11}