The ratio of the diameter of the sun to the d | vedclass

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(D) The angle $	heta$ subtended by the sun at the mirror is given by the ratio of the diameter of the sun $(D)$ to the distance between the earth and

Vedclass · Accepted Answer

$1.8 	imes 10^{-3} \ m$

Vedclass · Answer

(D) The angle $	heta$ subtended by the sun at the mirror is given by the ratio of the diameter of the sun $(D)$ to the distance between the earth and the sun $(d_{SE})$.Since the sun is at a very large distance,its image is formed at the focus of the concave mirror.The angular size $	heta$ is given by $	heta = \frac{D}{d_{SE}} = 0.009 \ rad$.The diameter of the image $(d)$ formed at the focal plane is given by $d = f 	imes 	heta$,where $f$ is the focal length of the mirror.The focal length $f$ is half of the radius of curvature $R = 0.4 \ m$,so $f = \frac{R}{2} = \frac{0.4}{2} = 0.2 \ m$.Substituting the values,we get $d = 0.2 \ m 	imes 0.009 = 0.0018 \ m$.Therefore,$d = 1.8 	imes 10^{-3} \ m$.

The ratio of the diameter of the sun to the distance between the earth and the sun is approximately $0.009$. The approximate diameter of the image of the sun formed by a concave spherical mirror of radius of curvature $0.4 \ m$ is

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