The filament of a light bulb has a surface area 64 mm2. The filament can be considered as a black body at temperature 2500 K emitting radiation like a point source when viewed from far. At night the light bulb is observed from a distance of 100 m. Assume the pupil of the eyes of the observer to be circular with radius 3 mm. Then (Take Stefan-Boltzmann constant = 5.67 × 10−8 Wm−2K−4, Wien’s displacement constant = 2.90 × 10−3m-K, Planck’s constant = 6.63 × 10−34Js, speed of light in vacuum = 3.00 ×108 ms−1) a) power radiated by the filament is in the range 642 W to 645 W b) radiated power entering into one eye of the observer is in the range 3.15 × 10−8 W to 3.25 × 10−8 W c) the wavelength corresponding to the maximum intensity of light is 1160 nm d) taking the average wavelength of emitted radiation to be 1740 nm, the total number of photons entering per second into one eye of the observer is in the range 2.75 × 1011 to 2.85 × 1011

The filament of a light bulb has a surface area 64 mm². The filament can be considered as a black body at temperature 2500 K emitting radiation like a point source when viewed from far. At night the light bulb is observed from a distance of 100 m. Assume the pupil of the eyes of the observer to be circular with radius 3 mm. Then (Take Stefan-Boltzmann constant = 5.67 × 10⁻⁸ Wm⁻²K⁻⁴,

Wien’s displacement constant = 2.90 × 10⁻³m-K,

Planck’s constant = 6.63 × 10⁻³⁴Js,

speed of light in vacuum = 3.00 ×10⁸ ms⁻¹)

a) power radiated by the filament is in the range 642 W to 645 W

b) radiated power entering into one eye of the observer is in the range 3.15 × 10⁻⁸ W to 3.25 × 10⁻⁸ W

c) the wavelength corresponding to the maximum intensity of light is 1160 nm

d) taking the average wavelength of emitted radiation to be 1740 nm, the total number of photons entering per second into one eye of the observer is in the range 2.75 × 10¹¹ to 2.85 × 10¹¹