- #1

- 95

- 7

- Homework Statement
- A train is traveling at a constant velocity v = 0.8c (80% of light speed). The figure shows a train observed from above. A light beam hits point P at the back of the wagon, from where the light is reflected in all directions. There are two questions that need to be answered;

1) I have to explain that some of the light has to be reflected obliquely (tilted, not in a straight line) backward, without hitting the wagon wall.

2) What is the maximal angle that the light beam can be reflected at

- Relevant Equations
- The formula for length contraction

$$L = \frac{L_0}{\gamma}$$

L_0 is the length of the object observed from the inertial frame of reference, gamma is the Lorentz factor

1) really does not make sense to me. It is not clear to me how light could be reflected in multiple directions if the source is not a tilted mirror or another object with specific properties. I think the thought of the "point" P confuses me. Further, the fact that light travels in the opposite direction initially from the velocity vector (direction of the moving train) does not give me any intuition. I suppose it would have to do something with contraction of the train, as I shall attempt in 2)

2) The correct solution that I came up with (which is 53 degrees) was by using the Lorentz factor. Namely, if we calculate

##y = 1/ \sqrt{1-0.8^{2}}##

we obtain a value of y = 5/3. Making a right triangle, We get the value of 53 degrees (I guess the hypothenause would be the refhypotenuse

My question then would be, what and how does this angle of reflection have anything to do with the Lorentz factor and possibly contraction? And if it can be used to potentially answer 1)