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Photometry — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsPhotometry1 Mark
Question
Figure shows a small diffused plane source S placed over a horizontal table-top at a distance of $2.4m$ with its plane parallel to the table-top. The illuminance at the point A directly below the source is $25$ lux. Find the illuminance at a point B of the table at a distance of $1.8m$ from A.
✓

Answer

Let $x$ be the distance moved.Let the illuminance of the candle and the lamp at a distance 1 m be $\mathrm{I}_{\mathrm{C}}$ and $I_L$ respectively. According to question
$\text{E}=\frac{\text{I}_\text{L}}{(8.0)^2}=\frac{\text{I}_\text{c}}{(0.2)^2}$
$\Rightarrow\frac{\text{I}_\text{L}}{\text{I}_\text{c}}=16$
Again after the wrapping the paper around
$\frac{49}{100}\frac{\text{I}_\text{L}}{(0.8+\text{x})^2}=\frac{\text{I}_\text{c}}{(0.2)^2}$
Either,
x = -0.24
or,
x = -1.36 this value is not acceptable because it is more than 0.8
so, x = 0.24m (-ve sign denotes distance is to be decreased).
x = 24cm

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