Suppose a light source is positioned in R at the origin (0, 0). Smooth mirrors are...

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Suppose a light source is positioned in R² at the origin (0, 0). Smooth mirrors are positioned along the lines y = 0 and y = 2 from x = 0 to x = 10. The light source is then oriented so that the beam of light emanating from it makes an angle, chosen uniformly and at random, of between 15° and 75° with the positive x-axis. The beam is then allowed to reflect back and forth between the two mirrors until it "exits the tunnel", that is, it crosses the line x = 10. If the expected distance that the beam of light travels from its source until it exits the tunnel 10 can be expressed as In(a+b√c), where a, b, c are positive integers with c square-free, then find a + b + c. πT Suppose a light source is positioned in R² at the origin (0, 0). Smooth mirrors are positioned along the lines y = 0 and y = 2 from x = 0 to x = 10. The light source is then oriented so that the beam of light emanating from it makes an angle, chosen uniformly and at random, of between 15° and 75° with the positive x-axis. The beam is then allowed to reflect back and forth between the two mirrors until it "exits the tunnel", that is, it crosses the line x = 10. If the expected distance that the beam of light travels from its source until it exits the tunnel 10 can be expressed as In(a+b√c), where a, b, c are positive integers with c square-free, then find a + b + c. πT

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