Question

In the “old days”, televisions were made from Cathode Ray Tubes whereby a beam of
electrons rapidly swept across the inside of the screen as a result of strategic deflections
from magnetic fields acting on the beam. Suppose that Frank has a massive 2000 inch
TV in which the image has to be updated 100 times per second (to minimize the
appearance of “flicker”) and that there are 100,000 rows.
(a) Show that the electron beam moves across the screen with a speed v  c .
(b) Explain why this superluminal speed does not contradict relativity. In particular, why
can’t information be transmitted from one side of the screen to the other with v  c ?

Answer 1

Realistically, the TV would be kind of useless.Let us assume that the electrons are travelling at the speed of light. When they hit the phosphor screen, they'll be imparting energy to the valence electrons which will subsequently move to a higher energy state. They come down to a lower energy state after releasing energy in the form of radiation. However, since the speed is c, and by subsequent calculation of the energy using the relativistic energy-momentum equation, The frequency of the llight emitted would not be in the visible spectrum.

But then this is a hypothetical situation.!!!

a) To find the speed :

1. we first have to find the distance the e beam travels,i.e the length of the screen.

• We know that the diagonal length is 2000 in.
• The aspect ratio of old TVs(i.e the ratio of width to height) is 4/3 .So let the length and breadth of the TV be 4x and 3x respectively.

• By Pythagoras theorem,

2000² = (4x)² + (3x)² = 16x² + 9x² = 25x²

--> or x² = (2000)²/25 --> x = 2000/5 = 400

Thus, length = 4x = 4*400 = 1600 inches = 40.64m

2. Now we must find the frequency of the electron beam. We know that the screen refresh rate is 100 times in a second. That means the electron beam has to travel across the entire screen (along the 100,000 lines) 100 times..

So the frequency of the beam must be 100 * 100,000 = 10^7

Or we can say that the time taken by the electron should be 10^-7 s (Time = 1/frequency)

SO, now we have the distance the electron beam has to travel, i.e 40.64m and the time = 10^-7 s

By that logic, the speed = distance/time = 40.64 / (10^-7) = 4.06 * 10^8 ms^-1