I have been staring at this problem for longer than I would like to admit.
I am trying to determine the path of a light ray from an object that is reflected from two plane mirrors and into the aperture of a pinhole camera. I have sketched the arrangement here.
- The ray starts at the known point D (the object)
- Then is reflected from the first plane mirror at unknown point C with unknown angle of incidence and reflection $\theta_C$
- Then is reflected from the second plane mirror at unknown point B with unknown angle of incidence and reflection $\theta_B$
- Finally the ray ends the known point A (the pinhole)
The point C lies on the surface of the first mirror, given by the known points G and H, and the point B lies on the surface of the second mirror, given by the known points E and F. To determine the light path, we need to find the two unknown points C and B.
To approach this problem, I have tried to solve for $\theta_C$ and $\theta_B$ by dividing my previous sketch into three (see here). From each sketch I find the following:
- $\theta_C=\pi-\widehat{CHD}^*-\widehat{HDC}$
- $\theta_B-\theta_C=\pi-\widehat{CGE}^*-\widehat{GEB}^*$
- $\theta_B=\pi-\widehat{BAE}-\widehat{AEB}^*$
where I have indicated known angles with a $^*$. But in these three equations, I have four unknowns. So I am missing something. I would be very grateful if someone could take the time to help me find the missing piece. Thank you.