derive mirror formula
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........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. In ABC and A1B1C <ABC = <A1B1C (right angles) <ACB = <A1CB1 <CAB = <CA1B (common angle) ABC is similar to A1B1CAB/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
........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. In ABC and A1B1C <ABC = <A1B1C (right angles) <ACB = <A1CB1 <CAB = <CA1B (common angle) ABC is similar to A1B1CAB/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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You can see that the triangles shaded are congruent
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