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Physics · UNITS AND MEASUREMENT
हिन्दीAs illustrated in Fig. 1.1(b), a solid angle \( d\Omega \) is defined as the ratio of intercepted area \( dA \) of a spherical surface to the square of its radius \( r^2 \). A flat circular disc of radius \( R \) is placed perpendicular to the axis at a distance \( d = \sqrt{3}R \) from an apex \( O \). The solid angle subtended by the disc at the apex \( O \) is:
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Correct answer · Option A
\( \pi (2 - \sqrt{3})\text{ sr} \)
Explanation
The solid angle subtended by a disc of radius \( R \) at distance \( d \) is \( \Omega = 2\pi (1 - \cos\alpha) \), where \( \tan\alpha = \frac{R}{d} = \frac{1}{\sqrt{3}} \implies \alpha = 30^\circ \). Thus, \( \cos\alpha = \frac{\sqrt{3}}{2} \), so \( \Omega = 2\pi (1 - \frac{\sqrt{3}}{2}) = \pi (2 - \sqrt{3})\text{ sr} \).
