Find the luminous intensity of the sun if it | vedclass

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(C) The illuminance $E$ produced by a source of luminous intensity $I$ at a distance $r$ is given by $E = \frac{I}{r^2}$.Let $L$ be the luminous inten

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$25 	imes 10^{26} \, cd$

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(C) The illuminance $E$ produced by a source of luminous intensity $I$ at a distance $r$ is given by $E = \frac{I}{r^2}$.Let $L$ be the luminous intensity of the sun and $r_s = 1.5 	imes 10^{11} \, m$ be the distance from the earth to the sun.Illuminance by the sun: $E_s = \frac{L}{(1.5 	imes 10^{11})^2}$.Let $I_b = 10000 \, cd$ be the intensity of the bulb and $r_b = 0.3 \, m$ be its distance.Illuminance by the bulb: $E_b = \frac{10000}{(0.3)^2}$.Since the illuminance is the same,$E_s = E_b$:$\frac{L}{(1.5 	imes 10^{11})^2} = \frac{10000}{(0.3)^2}$$L = \frac{10000 	imes (1.5 	imes 10^{11})^2}{(0.3)^2}$$L = \frac{10^4 	imes 2.25 	imes 10^{22}}{0.09}$$L = \frac{2.25 	imes 10^{26}}{0.09} = 25 	imes 10^{26} \, cd$.

Find the luminous intensity of the sun if it produces the same illuminance on the earth as produced by a bulb of $10000 \, cd$ at a distance of $0.3 \, m$. The distance between the sun and the earth is $1.5 \times 10^{11} \, m$.

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