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Old Dec 7th 2010, 03:19 AM   #1
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Spherical Concave Mirror

A spherical concave mirror (not parabolic) has a radius of 4 cm on which a ray is incident 3 cm from the principle axis, as shown in the figure. Since the mirror is not parabolic the ray doesn’t pass through the focus. After reflection on A and then on B, the ray crosses the principal axis at point P. Find the distance of P from C.

*The answer should be according to the following convention:
If the ray passes the principle axis left of C the distance is positive, else negative.
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Old Feb 13th 2011, 09:42 AM   #2
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Draw CD perpendicular to the parallel ray. Join CA and CB. Let ACF line intersects AB at E.
Now CD = 3 cm and CD = 4 cm. Let $\displaystyle \angleDAC$ be θ. So sinθ = 3/4.
Now angle DAC = CAF = CBF = CBP = θ.
Angle CFB = 2θ. And angle PCB = 3θ.Then angle CPB = 180 - 4θ.
Now use sine rule.
PC/sinθ = CB/sin(180 - 4θ.)
CB = 4 cm. Find PC.
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