Question 26: EM waves

Question

A point light source emits E.M. waves in free space. A detector, placed at a distance of $L \mathrm{~m}$, measures the intensity as $I_{\mathrm{o}}$. 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 $\_\_\_\_$ .

Accepted Answer

The intensity (I) of electromagnetic waves from a point source in free space follows the inverse square law.
$$ I=\frac{P}{4 \pi r^2} $$
Where P is the power of the source and r is the distance from the source.
Initial distance is L and the intensity recorded is $\mathrm{I}_0$.
It is given that the detector is shifted to another location on the same spherical surface.
On a spherical surface is all points are at a constant distance r from the center (the source).
Since the detector remains on the same spherical surface, its distance from the point source remains L .
The angle ( $45^{\circ}$ ) represents a change in direction, but not a change in distance r .
As r is constant $\mathrm{r}_1=\mathrm{r}_2=\mathrm{L}$ :
$$ I_{	ext {new }}=\frac{P}{4 \pi L^2}=I_0 $$
Therefore, the measured intensity at new location will be $\mathrm{I}_0$. Hence, the correct option is (B).

Answer

$\frac{I_{\mathrm{o}}}{4}$

Answer

$I_{\mathrm{o}}$

Answer

$\frac{I_0}{\sqrt{2}}$

Answer

${\frac{I_{\mathrm{o}}}{2}}$

EM waves

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