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Hi I'm working on a project where I need to calculate what angle a mirror needs to be at in order to reflect a source of light onto a particular location on a surface. A lot like this: Help finding solution for trigonometric equation

Only without the stuff about cylinders.

Judging by this diagram how can I solve for $C$? Ivella states that $c = \frac{a+b}{2}$ but I don't see how? Should it be $c= \frac{b-a}{2}$ ?

That seems more likely, though I'm not sure about that either.

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1 Answer

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Since angle of incident$=$ angle of reflection We get $ a+c=b-c$ ..............$ 1$

Also from figure we get $\frac{\pi}{2}-(b-c)-c=\tan^{-1} \frac{y}{x}$ Gives $\frac{\pi}{2}-b= \tan^{-1} \frac{y}{x}$ This gives $b$ and we know $a$ as it is our incident ray angle,so from $1$ we get $ c$

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