the sun (diameter d) subtends an angle x radians 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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so take this

Dear Student,
Please find below the solution to your problem.

The distance between sun and mirror is basically infinity.
∴ u = ∞
Now, on using mirror law, we get,
-1/f = 1/v + 1/u
On substituting the given values, we get,
-1/f = 1/v + 1/∞
-1/f = 1/v + 0
-1/f = 1/v
∴ -f = v
The 'negative sign' indicates real, inverted and diminished.
The sun subtends an angle θ radian at the pole, we get,
θ = r/f
Where, r is radius of image
r = θf
∴ d = 2r = 2fθ

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