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Question
An electric bulb is hanging over a table at a height of 1 m above it. The illuminance on the table directly below the bulb is 40 lux. The illuminance at a point on the table 1 m away from the first point will be about ___________ .
Options
10 lux
14 lux
20 lux
28 lux
Solution
14 lux
Here,
\[r = \sqrt{2}\]
\[\tan\theta = \frac{BC}{AB} = 1\]
\[ I_o = 40\text{ lux}\]
\[\theta = \tan^{- 1} \left( 1 \right) = {45}^0 \]
The illuminance is given by
\[E = \frac{I_o \cos\theta}{r^2}\]
\[ = \frac{40 \times \cos( {45}^0 )}{\left( \sqrt{2} \right)^2}\]
\[ = 14\text{ lux}\]
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