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

We can approach this by considering the concept of wavefronts in wave optics. A point source in free space creates spherical wavefronts. A wavefront is defined as a locus of points that have the same phase and, for a uniform medium, the same amplitude and intensity.

The detector is initially at a point on a wavefront of radius $L$. The intensity at any point on this specific wavefront is given as $I_0$. When the detector is shifted to another location on the "same spherical surface", it is essentially being moved to another point on the same spherical wavefront.

Because the source is isotropic (radiates equally in all directions) and the distance from the source remains $L$ (the radius of the sphere), the energy per unit area per unit time passing through that surface is constant at every point on the surface. Therefore, the angular position (whether $45^{\circ}$ or any other angle) does not affect the magnitude of the measured intensity. The intensity remains $I_0$.