ENG1005: Laser Escape Room - Physical Laws Report Writing - Engineering Assignment Help

Assignment Task:

The laser points upwards and towards a mirrored wall, making an angle of cos−1 the normal to the wall on which it is mounted and the vertical (as shown above). The movable mirror is reflective on both sides and can be positioned at any location (including any height) in the room. Initially it is placed in the corner of the room, with one edge in contact with a mirrored wall (highlighted by a bold green line segment in the sketch above) and another edge in contact with the floor (highlighted by a bold yellow line segment in the sketch above).

Some information about mirrors:
(A) The physical laws for a mirror are that

•  the reflected light ray is in the same plane as the incoming ray and the normal to the mirror the angle between the reflected ray and the normal to the mirror is the same as that between the the incoming ray and the normal to the mirror (usually stated as “the angle of reflection is equal to the angle of incidence”) (B) The formula for the reflection of a vector a in a plane with normal n is 

The following questions will help guide you to finding an appropriate place for the mirror.
1. Describe the coordinate system that you will use. Your coordinate system should be right-handed. Where is the origin? How are the axes aligned? You may find it useful to include a sketch of the coordinate system, but you should also give some description in sentences.
2. In your coordinate system, write down a vector representing the direction that the laser is pointing.
3. Write down a vector equation for the line representing the laser beam as it leaves the laser.
4. At what point does the laser beam hit a mirrored wall?
5. The laser light reflects perfectly off the mirrored wall. Write down a vector representing the direction that the laser beam points after reflection.
6. Now write down a vector equation for the line representing the reflected laser beam.
7. Find two vectors in the plane of the movable mirror and hence find a normal to the mirror. Regardless of the location of this mirror, this will always be its normal.
8. You will need to place this mirror somewhere along the path of the reflected laser beam to reflect it one more time. The beam reflects according to the description given above. Show that the formula in point (B) obeys the physical laws in point (A). Then use the formula to write down a vector representing the direction of the reflected laser beam.

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