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

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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