Question

The distance between the earth and the moon has been very accurately measured by reflecting laser light off special reflectors placed by the Apollo manned moon landings (a) A pulse of laser light is emitted from the earth, reflects off the moon and returns. If it takes 2.56s to complete this journey what is the distance from the earth to the moon? (b) The laser is then made to scan across the surface of the moon creating a spot that apparently moves faster than the speed of light. What is the minimum angular rotation speed of the laser? (Assume small displacements) (c) Why can this spot not transmit information between two points on the moon faster than light?

Answer 1

The solution is given in the attached image.

(a) total time = 2.56s let d be the distance b/w Earth and moon d = 2.56/2 times c = 3.84 times 10^8 m (b) d times theta = h, h rightarrow distance b/w points on moon w = d theta/df = (d)^-1 times du/dt so, for du/dt greaterthanorequalto c d theta/dt greaterthanorequalto (d)^-1 times c greaterthanorequalto 3 times 10^8/3.84 times 10^8 greaterthanorequalto 0.7812 rad/sec (c) Information is sent from laser to point and point to laser, not from point to point In order to send information from one point to other, laser has to know what information to send. So, to send information from one point to other, the process is point rightarrow laser rightarrow point which is clearly not faster than light

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