The sun (diameter d) subtends an angle theta | vedclass

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Question

(D) The sun is at an effectively infinite distance from the concave mirror,so the object distance $u = \infty$.Using the mirror formula: $\frac{1}{v}

Vedclass · Accepted Answer

$f 	heta$

Vedclass · Answer

(D) The sun is at an effectively infinite distance from the concave mirror,so the object distance $u = \infty$.Using the mirror formula: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$.Substituting $u = \infty$,we get $\frac{1}{v} + 0 = \frac{1}{f}$,which implies $v = f$.Thus,the image of the sun is formed at the focus $F$ of the concave mirror.Let $D_i$ be the diameter of the image formed at the focal plane.Since the angle subtended by the sun at the pole $P$ is $	heta$,the image formed at the focus also subtends the same angle $	heta$ at the pole.Using the definition of angle in radians,$	heta = \frac{	ext{arc length}}{	ext{radius}} = \frac{D_i}{f}$.Therefore,the diameter of the image is $D_i = f 	heta$.

The sun (diameter $d$) subtends an angle $\theta$ radian at the pole of a concave mirror of focal length $f$. What is the diameter of the image of the sun formed by the mirror?

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