Question

When observed from the earth the angular diameter of the sun is $$0.5$$ degree. The diameter of the image of the sun when formed in a concave mirror of focal length $$0.5\ m$$ will be about :

A
3.0 mm
B
4.4 mm
C
5.6 mm
D
8.8 mm

Solution

The correct option is B $$4.4\ mm$$  Given, Understand the angle subtended by the common tangents with Sun and its image are vertically opposite angles. Hence they are equal to each other and is equal to 0.5 degrees. Thus the angle $$\angle \,\text{BOA}={{0.5}^{o}}$$ Also the distance $$r=\,OA=OB=50\,\text{cm}$$ Hence the distance $$\mathrm { AB }$$ is $$AB=\theta r={{0.5}^{o}}\left( \dfrac{\pi }{{{180}^{o}}} \right)\times r$$ $$AB={{0.5}^{o}}\left( \dfrac{\pi }{{{180}^{o}}} \right)\times 50=0.44\,cm$$ Hence, diameter of sun on image is $$4.4\,mm$$Physics

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