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. If λ=532 nm, what is the minimum diameter of the circular opening from which the laser beam emerges? The earth-moon distance is 384,000 km.

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Physics

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3 June, 14:26

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. If λ=532 nm, what is the minimum diameter of the circular opening from which the laser beam emerges? The earth-moon distance is 384,000 km.

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Answers (1)

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Kaeden Cohen · Answer 1

d = 2,042 10-3 m

Explanation:

The laser diffracts in the circular slit, so the process equation is

d sin θ = m λ

The first diffraction minimum occurs for m = 1

We can use trigonometry in the mirror

tan θ = Y / L

Where L is the distance from the Moon to Earth

Since the angle is extremely small

tan θ = sin θ / cos θ

Cos θ = 1

tant θ = sin θ = y / L

We replace

d y / L = λ

d = λ L / y

Let's calculate

d = 532 10⁻⁹ 3.84 10⁶/1 10³

d = 2,042 10-3 m