# Physicists' Laser Show

Geometry Level 5

Consider yourself strolling through a unique and exciting carnival.

Suddenly you come across an interesting amusement labeled 'Laser Target Shoot'. The attendant guides you to a small rectangular chamber with walls covered with ideally reflecting mirrors. At your corner (Corner 1), there is a powerful laser locked into place, horizontally at an angle 45$$^{\circ}$$ to the walls. The attendant asks you to fire a shot.

The length of the chamber is 3536 cm while its breadth is 697 cm. Targets are placed at all the 4 corners of the room (including CORNER 1, from where the laser was fired)

Can you find out the number of reflections the laser beam will undergo before finally hitting one of the four targets and which target will it finally hit?

If the total number of reflections is $$a$$ and the corner number of the target which the laser will finally hit is $$b$$, give your answer as $$a+b$$.

Details and Assumptions

• All the 4 surfaces (walls) are perfectly reflecting.
• There is no loss of intensity of the laser beam whatever be the number of reflections.
• Targets have been placed at all the four corners i.e 1,2, 3 and 4 as marked in the figure.
• The laser beam will be fired only at the given angle and the given position i.e. it cannot be adjusted.

P.S. This is simple enough to be done manually, I don't approve of a computer-based solution.

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