# 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

Fawz Naim
37 Points
11 years ago

Devasish Bindani
45 Points
11 years ago

so take this

Shivang
13 Points
3 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
one year ago
Dear Student,

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