Scientists use laser range-finding to measure the distance to the moon with grea

Question

Scientists use laser range-finding to measure the distance to the moon with great accuracy. A brief laser pulse is fired at the moon, then the time interval is measured until the "echo" is seen by a telescope. A laser beam spreads out as it travels because it diffracts through a circular exit as it leaves the laser. In order for the reflected light to be bright enough to detect, the laser spot on the moon must be no more than 1.0 km in diameter. Staying within this diameter is accomplished by using a special large-diameter laser. Part A If = 540nm , what is the minimum diameter of the circular opening from which the laser beam emerges? The earth-moon distance is 384,000 km. Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

wo steps.
1) Calculate the angle subtended by 1.0 km at a distance of 384,000 from trigonometry by solving for A in TAN(A)=1/384,000 where A is the angle.
2) Then calculate the aperture size needed from the circular aperture Rayleigh Criterion formula which is SIN(A)=1.22W/D

SIN(A)=1.22*540/384,000=1.71*10^-3 where W is the wavelength (540 nm in this case) and D is the size you need to calculate. Be sure to use consistent units of measure for all quantities, which may require you to change units, like maybe change nm to meters or whatever.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.