Machine-translated by Google. Questions are authored in English.
Top

Discussion

An observer \(\bar{O}(\bar{t}, \bar{x})\) moves with a constant velocity in the positive \(x\)-direction relative to an observer \(O(t, x)\) at rest. In the frame of reference of \(\bar{O}(\bar{t}, \bar{x})\), a light-ray emitted at a point P at some time reaches the \(\bar{x}\)-axis at the point Q. Then, on reflection it arrives at point R, as shown in the figure.

Diagram in the barred frame: P on the t-bar axis below the origin, Q on the x-bar axis, R on the t-bar axis above, joined by a zigzag light path

Which of the following options represents these events as observed by \(O(t, x)\)?

  • A.Frame of O with t, x, t-bar and x-bar axes: P below the origin on the t axis, Q on the x-bar line and R on the t-bar line above the x axis, joined by a zigzag light path
  • B.Frame of O with Q on the x axis: P on the t axis below the origin and R on the t-bar line above, joined by a zigzag path through Q
  • C.Frame of O with Q on the x axis to the left of the origin, P on the t-bar line below and R on the t-bar line above, joined by a zigzag path
  • D.Frame of O with Q on the x-bar line, P on the t-bar line far below the origin and R on the t-bar line above, joined by a zigzag light path

Answer: D

The correct diagram is (D).

In the frame of \(\bar{O}\), P and R lie on the \(\bar{t}\) axis (\(\bar{x} = 0\)), before and after the reflection, and Q lies on the \(\bar{x}\) axis (\(\bar{t} = 0\)) at positive \(\bar{x}\). These facts hold in every frame, because they describe which events share a position or a time for \(\bar{O}\).

Since \(\bar{O}\) moves along \(+x\), its worldline, the \(\bar{t}\) axis, tilts towards \(+x\) in the diagram of \(O\), and its \(\bar{x}\) axis tilts upwards by the same angle, as a mirror image about the light line. So P and R must sit on the tilted \(\bar{t}\) line and Q on the tilted \(\bar{x}\) line, with Q on the right.

(A) puts P on the vertical \(t\) axis, not on the \(\bar{t}\) axis. (B) draws the \(\bar{x}\) axis on top of the \(x\) axis, which is the Galilean picture and ignores the relativity of simultaneity. (C) places Q on the negative side, which would need \(\bar{O}\) to move the other way. Only (D) has P, R on \(\bar{t}\), Q on \(\bar{x}\) and Q to the right.

No comment is present. Be the first to comment.
Loading…

Post your comment

Please log in or register to post a comment.

Subject Categories

Examination Categories

About Us

ExamsRepo

Copyright © 2026 ExamsRepo . All Rights Reserved . With