Two upright plane mirrors, 0.89 m tall, are placed parallel to each other 2.83 m apart. The top of the mirror on the right is then moved back a little so that its surface tilts away from the other mirror at an angle of 13.8° off the vertical. A narrow laser beam passes perpendicularly through a small hole in the very bottom of the mirror on the left and strikes the tilted mirror, from which it reflects. How many times will it reflect from the upright mirror?
The first returning beam is aimed up at 2x13.8 = 27.6 degrees. The next returning beam is aimed up at 55.2 degrees. After doubling the angle again, the beam will not return to the upright mirror.
The answer is twice
that answer was wrong.. :S
Your question is best solved graphically. That way, you can verify that each return beam does not pass over the top of the upright mirror.
It seems that, with that wide separation of short mirrors, even the first return beam will pass over the top of the upright mirror.
In that case, the answer is never.
that answer also turns out to be incorrect haha
ha ha to you. Draw the optical diagram.
To determine how many times the laser beam will reflect from the upright mirror, we need to consider the geometry of the setup.
First, let's identify the different elements in the problem:
- Mirror A: The upright mirror on the left (initial position).
- Mirror B: The tilted mirror on the right (moved back a little from the initial position).
- Laser Beam: The narrow laser beam passing through a small hole in the bottom of Mirror A and reflecting off Mirror B.
Based on the given dimensions, we have:
- Height of Mirror A = 0.89 m
- Distance between Mirrors A and B = 2.83 m
- Angle of Mirror B with the vertical = 13.8°
To solve this problem, we can break it down into steps:
Step 1: Determine the height where the laser beam strikes Mirror B.
- Since the laser beam passes through a small hole in the bottom of Mirror A, it will hit Mirror B at the same level as the hole.
- Therefore, the height where the laser beam strikes Mirror B is also 0.89 m.
Step 2: Calculate the distance between the point of reflection on Mirror B and the line connecting the two mirrors.
- To do this, we need to determine the horizontal displacement of the laser beam's point of reflection on Mirror B.
- This can be calculated using trigonometry.
- The horizontal displacement = (Height of Mirror B) * tan(angle of Mirror B)
- Height of Mirror B = Height of Mirror A = 0.89 m
- Angle of Mirror B = 13.8°
- Horizontal displacement = (0.89 m) * tan(13.8°)
Step 3: Calculate the number of reflections.
- To find the number of reflections, we need to determine how many times the laser beam will travel back and forth between the mirrors before it escapes.
- The number of reflections can be calculated by dividing the total distance traveled by the beam from one mirror to the other by the horizontal displacement calculated in Step 2.
- The total distance traveled by the beam = Distance between Mirrors A and B = 2.83 m
- Number of reflections = (Total distance traveled) / (Horizontal displacement)
Now, you can substitute the values into the above formulas and calculate the number of reflections.