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

Answer 1

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

\[E   =   \frac{I_o \cos\theta}{r^2}\]

\[         = \frac{40 \times \cos( {45}^0 )}{\left( \sqrt{2} \right)^2}\]

\[           = 14\text{ lux}\]