$\"\"$

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Illumination of the light is $\"\"$ .

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From the figure, $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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Derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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Illumination is maximum when $\"\"$ .

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Therefore,

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$\"\"$

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$\"\"$ or $\"\"$ .

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If $\"\"$ then $\"\"$ .

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Since $\"\"$ is acute angle.

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$\"\"$

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$\"\"$ .

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If $\"\"$ , then $\"\"$ .

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$\"\"$

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Substitute above result in $\"\"$ .

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$\"\"$

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$\"\"$

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Height of the light source is $\"\"$ feet.