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CBSE Class 10 Answered

Prove mathematically that r=2f for mirror.  
Asked by shyamala.holla3 | 16 Feb, 2018, 03:35: PM
answered-by-expert Expert Answer
Let us refer the above figure to prove focal distance is half of radius of curvature.
 
Let us consider a parallel ray RQ passing through focal point F after reflection. Let us join QC. 
begin mathsize 12px style angle R Q C space equals space angle Q C F space equals space theta space b e c a u s e space R Q space i s space p a r a l l e l space t o space C F
angle R Q C space equals space angle C Q F space equals space theta space left parenthesis l a w space o f space r e f l e c t i o n right parenthesis
h e n c e space angle Q C F space equals space space angle C Q F space equals space theta space a n d space triangle Q C F space i s space i s o c e l e s s
h e n c e space C F space equals space F Q
f o r space m i r r o r space o f space l a r g e space r a d i u s space o f space c u r v a t u r e comma space F Q space almost equal to space F P space
h e n c e space C F space equals space F P space a n d space F P space equals space 2 cross times C P
i. e space r space equals space 2 f end style
Answered by Thiyagarajan K | 16 Feb, 2018, 05:40: PM
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