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Exercise 2 ZCT 1042025 A.pdf
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6. The light bulb's filament, with dimensions of length \( 1=20 \mathrm{~mm} \) and radius \( \mathrm{r}=0.05 \mathrm{~mm} \), is maintained at a temperature \( \mathrm{T}=5000 \mathrm{~K} \) by an electric current. Acting as a blackbody, it emits radiation isotropically. During the night, while observing the light bulb from a distance \( \mathrm{D}=10 \mathrm{~km} \), the pupil of your eye is fully dilated to a radius \( \mathrm{r}_{\mathrm{eye}}=3 \mathrm{~mm} \). Determine:
(i) The total power radiated by the filament.
(ii) The radiation power entering your eye.
(iii) The wavelength at which the filament radiates the most power.
(iv) The number of radiated photons entering your eye every second, considering the average wavelength for the radiation as \( \lambda=600 \mathrm{~nm} \).
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