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A rectangular mirror with vertices A(0,0), B(100,0), C(100,1) and D(0,1) has holes at all four vertices. A ray of light incident from (–1, –1) in the direction of A, entered inside the rectangle. After how many collisions, it exits from the rectangle?

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answer is 99.

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Detailed Solution

y = x at y =1, x =1

Again y – 1 = –(x – 1)

x + y = 2
y = 0, x = 2 And so on
Collision $\underset{}{\to}$ on y = 1
(1, 1), (3, 1), …….(99, 1) Total 50
Collision $\underset{}{\to}$ on y = 0
(2, 0), (4, 0) ……. (98,0) Total 49
Total collision - 99

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