If sun rays coming from solar disc makes an angle of 0.63 degree at the pole of a concave mirror of radius 400 cm, then what will be size of the image give solution with explanation..
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Answers
Answer:AB= Ds is diameter of sun. The sun being at infinity , the image will be formed at focus F. The diameter of image is Di.Angle Q is small. Therefore, object distance, u= Ds/<Q.
Di/Ds= magnification = v/u=f/u=R/2u.
Therefore, Di=(R/2u)Ds=(R/2Ds/Q))Ds.= (1/2)QxR OR
Di=(1/2)Q(2f)=Qxf
Explanation:
The size of image of sun is 2.2 cm.
The sun rays coming from solar disc makes an angle of 0.63° at the pole of a concave mirror of radius 400cm.
We have to find the size of the image of sun.
First we should convert angle into radian.
We know, 180° = π rad
⇒ 0.63° = 0.63π/180 rad (very small angle)
Now see the diagram shown in answer, Here an sun rays makes an angle θ = 0.63° at the pole of concave mirror and d is the size (diameter) of the image of sun.
We know,
- sun rays converges after reflection from a concave mirror at a point called focus.
- and the distance from the pole of mirror to the focus is the focal length, f.
Here, it is clear that, tan(θ/2) = (d/2)/f
but angle is very small so, tan(θ/2) ≈ (θ/2)
∴ θ/2 = (d/2)/f
⇒ θ = d/f
Here focal length of concave mirror , f = radius of curvature of concave mirror/2 = 400/2 = 200 cm
∴ 0.63π/180 = d/200cm
⇒ d = 2.198 cm ≈ 2.2 cm
Therefore the size of image is 2.2 cm.
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