Question

Sunlight of intensity $1.3kW{m}^{-2}$ is incident normally on a thin convex lens of focal length $20cm$. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light, in $kW{m}^{-2}$, at a distance $22cm$ from the lens on the other side is _____.

Answer 1

$\frac{r}{R}=\frac{2}{20}=\frac{1}{10}$

$\therefore$ Ratio of area $={\left(\frac{r}{R}\right)}^2=\frac{1}{100}$
Let energy incident on lense be E.
$\therefore$ Given $\frac{E}{A}=1.3$

To calculate: final $\frac{E}{a}$
$E=a\times 1.30$
Also $\frac{a}{A}=\frac{1}{100}$
$\therefore$ Average intensity of light at $22cm=\frac{E}{a}=\frac{A\times 1.3}{a}=100\times 1.3=130kW/m^2$