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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

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











Grade:9

4 Answers

Fawz Naim
37 Points
13 years ago

 

Devasish Bindani
45 Points
13 years ago

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so take this

Shivang
13 Points
5 years ago
Since the object distance → so, the Image can be assumed to form at the focus. So,
r/f = tan(x/2)
where r is the radius of image, and “x” is the angle substended by the object, i.e. Sun.
So, d = 2r = 2ftan (x/2)
Rishi Sharma
askIITians Faculty 646 Points
3 years ago
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

Thanks and Regards

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