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CBSE Class 10 Answered

why R=2f??? state the reason.
Asked by edayoor | 11 Aug, 2018, 09:45: PM
answered-by-expert Expert Answer
I assume the question is related to spherical mirror, Radius of curvature is twice of focal length.
 
As shown in figure, let us consider a ray parallel to axis of concave mirror that incident on P and after reflection passing through focal point F.
 
Let OP and OC are radius of curvature. If angle i as shown in figure is angle of incidence, then by law of reflection angle i equals angle r.
 
angle i and angle θ are equal because AP is parallel to OC. Hence angle r and angle θ are equal and the ΔFOP is isoceless triangle. 
Hence FP = FO. If the ray AP is very near to OC we can consider FP ≈ FC
 
Hence FC = OF = (1/2)OC or f = (1/2)R  or R = 2f
 

Answered by Thiyagarajan K | 13 Aug, 2018, 03:39: PM

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