Math, asked by ankushPatel9621, 10 months ago

good morning guys.

please derive the mirror formula ​

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Answered by jhaji27
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Chayanika Guin

Nov 16, 2013

what is the derivation of mirror formula of concave and convex mirror?

what is the derivation of mirror formula of concave and convex mirror?

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person

Priyanshu

Consider the shown figure where O is a point object and I is corresponding image. CB is normal to the mirror at B. By laws of reflection, For small aperture of the mirror, (Paraxial approximation) Applying sign convention,� If, but by definition, if Hence,������������ For convex mirrors, an exactly similar formula emerges.

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Agam Gupta

Derivation of formula for convex mirror: Let AB be an object placed on the principal axis of a convex mirror of focal length f. u is the distance between the object and the mirror and v is the distance between the image and the mirror. convex mirror formula In ABC and A1B1C <ABC = <A1B1C (right angles) <ACB = <A1CB1 <CAB = <CA1B (common angle) ABC is similar to A1B1C AB/A1B1 = BC/B1C........(1) similarly DEF issimilar to A1B1F DE/A1B1 = EF/B1F....(2) But DE = AB and when the aperture is very small EF = PF Equation (2) becomes AB/A1B1 = PF/B1F....(3) Frm equations (1) and (3) get PF/B1F = BC/B1C PF/PF-PB1 = PB + PC/PC - PB1 f/f - v = -u + 2f/2f - v [PF = f, PB1 = v, PB = u, PC = 2f] 2(2f - v)= (f-v)(2f-u) i could not write the following 2 steps sorry -vf + uf + 2 fv -vu=0 fv+uf-vu=0....(4) Dividing both sides of equation(4) by uvf we get fv/uvf + uf/uvf - uv/uvf=0 1/u +1/v - 1/f=0 1/u + 1/v = 1/f

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