Optical Delay - I

Geometry Level 2

An optical delay system consisting of two parallel, vertical mirrors is shown in the diagram. This system is used as a delay line for a laser beam.

The laser beam enters the system from point $A,$ bounces around on the two mirrors, and eventually exits from point $B$ after 99 reflections.

Find $\left \lfloor AB \right \rfloor.$

72 86 88 128

1 solution

Musab Fadel
Nov 14, 2017

X = tan (10) x 5 , AB = 100 X

Can someone tell me why this is the case? @David Vreken Sir, @Arjen Vreugdenhil Sir, please help!

Vinayak Srivastava - 11 months ago

If you look at the right triangle at the bottom of the diagram (where $\angle A$ is $10°$ ), the height is $5 \tan 10°$ . Along the length $AB$ there are $100$ of these heights, so the answer is $\lfloor 500 \tan 10° \rfloor = \boxed{88}$ .

David Vreken - 11 months ago

Oh, thank you Sir! Now I understand.

Vinayak Srivastava - 11 months ago

Optical Delay - I

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