Calculate Beam's Divergence Angle from Earth to Moon

In summary, a tiny laser beam from Earth is directed at the moon with a diameter of 2.50 m. The divergence angle of the beam can be calculated using the formula theta=s/r, where s is the diameter and r is the distance from the Earth to the moon. With a distance of 3.8x10^8 m, the calculated angle is 6.6x10^-9 rad. The use of the diameter as "s" in the formula can be explained by imagining a line from the eye to the bottom of the moon, with the diameter being at a right angle to that line. Alternatively, the radius can also be used, with the tangent of half the angle being (s/2)/
  • #1
mars shaw
10
0

Homework Statement


A tiny laser beam is directed from Earth to moon. If beam's diameter is 2.50 m at the moon, how small much the divergence angle be for the beam? The distance of moon from the Earth is 3.8x10^8 m




Homework Equations



The Attempt at a Solution

 
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  • #2
Hi Mars shaw! :wink:

(try using the X2 tag just above the Reply box :wink:)

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
  • #3
mars shaw said:

Homework Statement


A tiny laser beam is directed from Earth to moon. If beam's diameter is 2.50 m at the moon, how small much the divergence angle be for the beam? The distance of moon from the Earth is 3.8x10^8 m




Homework Equations


theta=s/r

The Attempt at a Solution


s=diameter=2.50 m
r=distance of moon from earth=3.8x10^8
theta=s/r
theta=2.50/3.8x10^8 = 6.6x10^-9 rad
I got the correct answer but I am confuse about diameter that how it can be taken as "s"?
Kindly explain.
 
  • #4
Hi Mars shaw ! :smile:

Because you imagine the line from your eye to the bottom of the moon as being length r, and the diameter (s) of the moon as being at right-angles to that line, so the tangent of the angle is s/r.

(and if you're not happy about that, but you'd rather use the radius, and the line to the centre of the moon, you'll get the same result: the tangent of half the angle is (s/2)/r :wink:)
 

FAQ: Calculate Beam's Divergence Angle from Earth to Moon

What is the significance of calculating the beam's divergence angle from Earth to Moon?

Calculating the beam's divergence angle from Earth to Moon is important for understanding the spread of a laser or radio beam as it travels through space. This information is crucial for designing communication systems and accurately targeting objects in space.

How is the beam's divergence angle measured?

The beam's divergence angle is typically measured in degrees and can be calculated using the distance between the source and target, the wavelength of the beam, and the size of the beam at the source.

What factors influence the beam's divergence angle?

The beam's divergence angle can be influenced by a variety of factors, including the type of beam (e.g. laser or radio), atmospheric conditions, and the quality of the optics used to generate the beam.

Is the beam's divergence angle constant over the entire distance from Earth to Moon?

No, the beam's divergence angle typically increases as the distance between the source and target increases due to the spreading of the beam over long distances. However, this can be mitigated by using high-quality optics and precise targeting.

How does the beam's divergence angle affect communication with objects in space?

The beam's divergence angle can significantly impact communication with objects in space. A larger divergence angle means that the beam will spread out more, making it more difficult to accurately target and communicate with objects at a distance. This is why precise calculation and control of the beam's divergence angle is crucial for successful communication with objects in space.

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