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

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(A) The sun is at a very large distance from the mirror,so the rays coming from the sun are parallel to the principal axis.These rays will focus at th

Vedclass · Accepted Answer

$f 	heta$

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(A) The sun is at a very large distance from the mirror,so the rays coming from the sun are parallel to the principal axis.These rays will focus at the focal plane of the mirror.The image of the sun is formed at the focal plane.From the geometry of the setup,the angle subtended by the sun at the pole is $	heta$.Since the image is formed at the focal plane at a distance $f$ from the pole,we can use the relation: $	ext{Angle} = \frac{	ext{Arc}}{	ext{Radius}}$.Here,the arc corresponds to the diameter of the image $(d)$ and the radius corresponds to the focal length $(f)$.Therefore,$	heta = \frac{d}{f}$.Thus,the diameter of the image is $d = f 	heta$.

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

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