If temperature of $Sun =6000\, K ,$ radius of Sun is $7.2 \times 10^{5}\, Km$ radius of Earth $=6000 \,Km \&$ distance between earth and $Sum =15 \times 10^{7}\, Km .$ Find intensity of light on Earth.
AIIMS 2019, Medium
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Consider the following figure.
The expression of total energy emitted by Sun is given by,
$E =\sigma T ^{4}\left(4 \pi R ^{2}\right)$
The expression of total energy received by Sun is given by,
$E ^{\prime}=\frac{\sigma T ^{4}\left(4 \pi R _{ s }^{2}\right)}{4 \pi d ^{2}} \pi\left( R _{e}\right)^{2}$
$=\frac{\sigma T ^{4} R _{ s }^{2}}{ d ^{2}}\left(\pi R _{ e }^{2}\right)$
Substitute the values.
$E ^{\prime}=\frac{\left(5.67 \times 10^{-8}\right)(6000)^{4}\left(7.2 \times 10^{8}\right)^{2}(3.14)\left(6000 \times 10^{3}\right)}{\left(1.5 \times 10^{11}\right)^{2}}$
$=19.2 \times 10^{16}$
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