Question

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?

Answer 1

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