The sun subtends an angle of 0.5^{circ} at th | vedclass

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(B) The angular diameter of the sun is given as $	heta = 0.5^{\circ}$.To use this in the formula, we convert the angle into radians:$	heta = 0.5^{\c

Vedclass · Accepted Answer

$4.36$

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(B) The angular diameter of the sun is given as $	heta = 0.5^{\circ}$.To use this in the formula, we convert the angle into radians:$	heta = 0.5^{\circ} 	imes \frac{\pi}{180^{\circ}} \ 	ext{radians}$.When a distant object like the sun forms an image at the focal plane of a convex lens, the diameter of the image $d$ is related to the focal length $f$ and the angular diameter $	heta$ by the relation:$	heta = \frac{d}{f}$Given $f = 50 \ 	ext{cm} = 0.5 \ 	ext{m}$.Substituting the values:$d = f 	imes 	heta = 0.5 \ 	ext{m} 	imes 0.5^{\circ} 	imes \frac{\pi}{180^{\circ}}$$d = 0.5 	imes 0.5 	imes \frac{3.14159}{180} \ 	ext{m}$$d \approx 0.004363 \ 	ext{m}$$d \approx 4.36 \ 	ext{mm}$.

The sun subtends an angle of $0.5^{\circ}$ at the earth's surface. Its image is formed by a convex lens of focal length $50 \ \text{cm}$. The diameter of the image will be (in $\text{mm}$)

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