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Alex787 [66]
2 years ago
13

The intensity of a light source at a distance is directly proportional to the strength of the source and inversely proportional

to the square of the distance from the source. Two light​ sources, one five times as strong as the​ other, are 16 m apart. At what point on the line segment joining the sources is the intensity the​ weakest?
Mathematics
1 answer:
jolli1 [7]2 years ago
5 0

Answer:

x=\frac{16}{\sqrt[3]{2}+1 }

Step-by-step explanation:

Q= illumination

I = intensity

Q= I/d^2

Q_total = \frac{I_1}{d_1^2}+\frac{I_2}{d_2^2}

= \frac{I}{x^2}+\frac{2I}{(16-x)^2}

now Q' = 0

⇒I{-\frac{2}{x^3}}+\frac{4}{(16-x)^3}

x=\frac{16}{\sqrt[3]{2}+1 }

[/tex]\frac{1}{x^3} = \frac{2}{(16-x)^3}

x=\frac{16}{\sqrt[3]{2}+1 }

is the required point

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Here is a rectangle which has a width of x cm. x cm
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