Question

In the figure shown, $O$ is a point source of light and $S$ is a screen placed at a distance $L$ from the source. The intensity of light at point $\text{A}$ on the screen due to the source is $81I$ , where $I$ is some unit. Now a large mirror $\left(M\right)$ is placed behind the source at a distance $L$ from it. The mirror reflects $100\%$ of the light energy incident on it. The intensity at point $A$ is $nI.$ The value of $n$ is (integer only)

Answer 1

Imagine the image of $O$ to be another point source. The mirror reflects the light as if it is diverging from the image. The wavefronts around a point source are spherical in shape and the intensity falls off with distance $\left(x\right)$ from the source as $$I\propto \frac{1}{x^2}$$Image as a source, is at a distance $3L$ from the point $\text{A}$.

$\therefore$ Intensity due to it will be ${\frac{1}{9}}^{th}$ of that caused by the original source.

$\therefore$ Intensity at $A=81I+\frac{81I}{9}=90I$

$\therefore n=90$