InterviewSolution
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InterviewSolution
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(a) With the help of a suitable ray diagram, derive the mirror formula for a concave mirror. |
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Answer» Solution :Mirror Formula for Concave Mirror : LET, AB be the length of an object placed beyond C in front of a concave mirror. The image A 'B' is REAL, inverted and between C and F. Applying sign conventions, we have object distance `PB=-u`, image distance `PB'=-v`, focal length `PF=-f` and radius of curvature `PC=-2f`. In similar `Delta s` ABC and A' B' F `(AB)/(A'B')=(BC)/(B'C)` ...(i) and in similar `Delta s` RSF and A' B' F `(RS)/(A'B')=(SF)/(B'F)"":' ""RS=AB` `(AB)/(A'B')=(SF)/(B'F)` ...(ii) From eq. (i) and (ii), we have `(BC)/(B'C)=(SF)/(B'F)` Since, the aperture of the concave mirror is small so the point S and P coincides. `:. (BC)/(B'C)=(PF)/(B'F)` `(PB-PC)/(PC-PB')=(PF)/(PB'-PE)` `(-u+2f)/(-2f+v)=(-f)/(-v+f)` `UV-uf-2vf+2f^(2)=2f^(2)-fv` `implies uv=uf+vf` Dividing both sides by `uvf`, we get `(uv)/(uvf)=(uf)/(uvf)+(vf)/(uvf)"":.""1/f=1/v+1/u`. 
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