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Derive the relation between f and R for a spherical mirror. |
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Answer» Solution :Let C be the centre of curvature of the mirror. Consider a light RAY parallel to the PRINCIPAL axis is incident on the mirror at M andpassesthrough theprincipal focus F after reflection. The geometry of reflection of the incident ray is shown in figure. The line CM is the normal to the mirrorat M. Let i be the angle of incidence and same will be the angle of reflection. If MP is the perpendicular from M on the principal axis, then from the geometry. The angles `angle MCP = i and angle MFP = 2i` From right angle trianagles `DeltaMCP and Delta MFP`. `tan i = (PM)/(PC) and tan2i = (PM)/(PF)` Asthe angles are small, `tiapproxi,i=(PM)/(PC)and2i=(PM)/(PF)` Simplifying further, `2(PM)/(PC) = (PM)/(PF):2PF=PC` PF is focal lenght f and PC is the radius of curvature R. `2f = R (or) f = (R)/(2)` `f = (R)/(2)` is the relation between f and R. 
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