In laser physics, a "white cell" is a mirror system that acts as a delay line for the laser beam. The beam enters the cell, bounces around on the mirrors, and eventually works its way back out. The specific white cell we will be considering is a circle with the equation x2 + y2 = 100 The section corresponding to −0.01 ≤ x ≤ +0.01 at the top is missing, allowing the light to enter and exit through the hole at point (-5.8.66).
The light beam in this problem starts at the point (1.0,9.95) just outside the white cell, and the beam has a slope of first impacts the mirror at (2,-6). Each time the laser beam hits the surface of the circle, it follows the usual law of reflection "angle of incidence equals angle of reflection." That is, both the incident and reflected beams make the same angle with the normal line at the point of incidence. In the figure, the red line shows the first two points of contact between the laser beam and the wall of the white cell; the blue line shows the line tangent to the circle at the point of incidence of the first bounce. The slope m of the tangent line at any point (x,y) of the given circle is: m = −x/y The normal line is perpendicular to this tangent line at the point of incidence.
How many times does the beam hit the internal surface of the white cell before exiting?
output :
8 -6
-9.96755 -0.21445
-9.96755 -0.21445
7.754234 6.248889
7.754234 6.248889
-7.04636 -7.06623
-7.04636 -7.06623
7.063139 7.078951
7.063139 7.078951
-7.06315 -7.07897
-7.06315 -7.07897
7.063153 7.078974
7.063153 7.078974
-7.06315 -7.07897
-7.06315 -7.07897
7.063153 7.078974
7.063153 7.078974
-7.06315 -7.07897
-7.06315 -7.07897
7.063153 7.078974
The number of reflections exceeds the limit
I have uploaded a pdf containing all handwritten equations to reach the solution, The solution I have reach is in this particular situation,