Sunlight of intensity is incident normally on a thin convex lens of focal length 20 cm. 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 , at

Question

Sunlight of intensity $1.3 kW m^{- 2}$ is incident normally on a thin convex lens of focal length 20 cm. 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 22 cm from the lens on the other side is _______. [2018]

Smart Achievers · Accepted Answer

(130)

Let $D$ be the initial area covered by light and $d$ be the final area covered by light at 22 cm.

From the figure, $∆ A F B$ and $∆ C F D$ are similar.

$∴$ $\frac{d}{D} = \frac{2}{20} = \frac{1}{10}$

$∴$ $Ratio of area = \frac{d^{2}}{D^{2}} = \frac{1}{100}$

As there is no energy loss, $∴$ $I_{0} D^{2} = I d^{2}$

$∴$ Average intensity of light at a distance of 22 cm

$I = \frac{D^{2}}{d^{2}} I_{0} = 1.3 \times 100 = 130.00 {kW m}^{- 2}$

Solution

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