Use the exact values you enter in previous answer(s) to make later calculation(s

Question

Use the exact values you enter in previous answer(s) to make later calculation(s). Using the Apache Point Observatory Lunar Laser-Ranging Operation (see the figure below), the distance to the Moon is determined by how long it takes for a laser pulse to travel from the Earth to the Moon and then reflect back to the Earth from special reflector arrays placed there by the Apollo astronauts. A 2.3-W laser sends 20 pulses per second (each only 100 picoseconds long) at a wavelength of 532 nm. Due to atmospheric absorption and dispersion of the beam, only a very faint reflected pulse arrives back at the observatory with a power of 3.0 10-17 W. (a) How many photons does the observatory send in an outgoing pulse? (b) How many photons are received in a returning pulse? (c) How many photons are sent for every one that is detected upon return?

Explanation / Answer

Here,

power sent , Po = 2.3 W

number of pulses , n = 20 per second

t = 100 ps

wavelength = 532 nm

Pin = 3 *10^-17 W

a) let the number of photons in outgoing photons is N

energy of single photon , E = h * c/wavelength

E = 6.626 *10^-34 * 3 *10^8/(532 *10^-9)

E = 3.737 *10^-19 J

number of outgoing photons on each pulse = 2.3 * 100 *10^-12/(3.737 *10^-19 )

number of outgoing photons on each pulse = 6.16 *10^8

number of outgoing photons on each pulse is 6.16 *10^8

b)

for the received pulse

number of received photons on each pulse = 2.3 * 3 *10^-17(3.737 *10^-19 )

number of received photons on each pulse = 184.6

number of received photons on each pulse is 184.6

c)

number of photons that are sent for one received = number of outgoing photons/number of received photons

number of photons that are sent for one received = 6.16 *10^8/(184.6)

number of photons that are sent for one received = 3.336 *10^6

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