InterviewSolution
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InterviewSolution
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Give relation between focal length and radius of curvature for spherical mirror. |
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Answer» Solution :Let C be the centre of curvature of the mirror. Consider a ray parallel to the principal axis striking the mirror at M. Then CM will be PERPENDICULAR to the mirror at M. Let `theta` be the angle of incidence and MD be the perpendicular from M on the principal axis. Then `angleMCP = theta" and "angleMFP = 2theta` Because, `DeltaMCP` is an obtuse angle for `angleMCP" and "angleMCF" and "angleCMF` are its internal angles. `DeltaMDC" and "DeltaMDF` are equiangular. [D `~~` P] `therefore tan theta=(MD)/(CD)" and "tan2theta=2theta` For small `theta`,which is true for paraxial rays, `tan theta ~~ theta" and "tan 2theta ~~ 2theta` `therefore theta=(MD)/(CD)" and "2 theta=(MD)/(FD)` ... (1) Now, for small 8, the point D is very close to the point P. Therefore, CD = CP = R and FD = FP = f From equation (1), `2theta=(MD)/(FD)` `therefore 2 theta=(MD)/(f)`... (2) and `theta=(MD)/(CD)` `therefore theta=(MD)/(R)`... (3) `therefore` From equation (2) and (3), `2xx(MD)/(R)=(MD)/(f)` `therefore 2f=R` `therefore` R=2f or f=`R/2` This relation is true for both CONCAVE and convex mirrors. |
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