Question

A point source of light $S$ is placed in front of a perfectly reflecting mirror as shown in the figure. is a screen. The intensity at the center of the screen is found to be? If the mirror is removed, then the intensity at the center of the screen would be?
A. $I$
B. $\dfrac{I}{g}$
C. $\dfrac{{9I}}{{10}}$
D. $2I$

Answer 1

Hint: You can start by calculating the intensity of light at the center of the screen when the mirror is present. This can be done by using the equation $I = \dfrac{K}{{{d^2}}}$ to calculate the intensity of light due to the light directly from the point source and the light that is reflected from the mirror and add them. Then calculate the intensity of light at the center of the screen when the mirror is not present by again using the equation $I = \dfrac{K}{{{d^2}}}$. Then compare the intensity of light at the center of the screen when the mirror is present and the intensity of light at the center of the screen when the mirror is not present to reach the solution.

Complete step by step answer:
Here, we are given two cases in the problem

Case 1 – When there is a reflecting mirror (plane mirror in this case) present.
In this case light from the point source of light will strike the center of the screen directly and the light from the point source of light $S$ will also strike the center of the screen after being reflected by the reflective mirror.
We know that intensity of light at any point is
$I \propto \dfrac{1}{{{d^2}}}$
$I = \dfrac{K}{{{d^2}}}$
Here,
$d = $ Distance of the point from the source
$K = $ Proportionality constant
The intensity of light from the point source $S$ that hits directly at the center of the screen is
${I_1} = \dfrac{K}{{d_1^2}}$
${I_1} = \dfrac{K}{{{a^2}}}$
The intensity of and the light from the point source of light $S$ that strikes indirectly the center of the screen after being reflected by the reflective mirror is
${I_2} = \dfrac{K}{{d_2^2}}$
${I_2} = \dfrac{K}{{{{(a + 2a)}^2}}}$
${I_2} = \dfrac{K}{{9{a^2}}}$
Total intensity of light at the center of the screen is
$I = {I_1} + {I_2} = \dfrac{K}{{{a^2}}} + \dfrac{K}{{9{a^2}}}$
$I = \dfrac{{10K}}{{9{a^2}}}$ (Equation 1)

Case 2 - When there is no reflecting mirror present.
In this case light from the point source of light will strike the center of the screen directly.
And we already know that, the intensity of light from the point source $S$ that hits directly at the center of the screen is
${I_1} = \dfrac{K}{{{a^2}}}$ (Equation 2)
Dividing equation 2 by equation 1, we get
$\dfrac{I}{{{I_1}}} = \dfrac{{\dfrac{{10K}}{{9{a^2}}}}}{{\dfrac{K}{{{a^2}}}}}$
${I_1} = \dfrac{{9I}}{{10}}$
Hence, the correct answer is option C.

Note:
Plane mirror is essentially a rectangular glass slab with a really smooth surface and is coated on one side by silver. Plane mirrors always produce an upright, virtual image. The size of the image is the same size as the object. The distance of the image from the plane mirror is the same as the distance of the object from the mirror.