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Question
A point source emitting light uniformly in all directions is placed 60 cm above a table-top. The illuminance at a point on the table-top, directly below the source, is 15 lux. Find the illuminance at a point on the table-top 80 cm away from the first point.
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Solution
Given,
Distance of the source from the table-top (r) = 60 cm or 0.6 m
Let Io be the intensity of illumination.
Illuminance directly below the source (EA) is given by,
`E_A=I_0/(0.6)^2`
⇒ I0 = 15 × (0.6)2
= 5.4 candela
Let EB be the illuminance at a point 80 cm away from the initial point.
So, `E_B=(I_0 costheta)/(OB)^2`
From the figure, we get
`cos theta=0.6/1`
OB = 1 m
Substituting the respective values in the above formula, we get
` E_B= 5.4(0.6/1)`
= 3.24 lux
So, the illuminance at a point on the table-top 80 cm away from the first point is 3.24 lux.
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