Question

A point light source emits E.M. waves in free space. A detector, placed at a distance of $L$ m, measures the intensity as $I_0$. The detector is now shifted to another location on the same spherical surface ensuring the angle between original location and new location as $45^{\circ}$. The measured intensity at new location will be ————.

• A. $I_0 / 4$
• B. $I_0$
• C. $I_0 / \sqrt{2}$
• D. $I_0 / 2$

Hint:

Intensity from a point source depends only on the distance from the source. If the distance doesn't change, the intensity remains constant.

Answer 1

The Correct Option is B

For a point source emitting electromagnetic waves uniformly in all directions, the intensity $I$ at a distance $r$ from the source is defined as the power $P$ per unit area of the wavefront. Since the waves spread out spherically, the area of the wavefront at distance $r$ is $4\pi r^2$. Thus, the intensity formula is:
$$I = \frac{P}{4\pi r^2}$$
From this relationship, we can see that the intensity depends inversely on the square of the distance from the source. Initially, the detector is at a distance $L$, so the intensity is:
$$I_0 = \frac{P}{4\pi L^2}$$
The problem states that the detector is moved to a new location on the "same spherical surface". By definition, every point on a spherical surface is at the same distance from its center. In this case, the light source is at the center, so the distance to the new location is still $L$.

The angular displacement of $45^{\circ}$ describes the shift along the surface, but it does not change the radial distance $r$. Since the distance $r$ remains constant at $L$, the intensity measured at the new location will be the same as the original intensity, which is $I_0$.