A laser beam is directed at the Moon, 380,000 km from Earth. The beam diverges at an angle of 6.2×10−5 rad. What diameter spot will it make on the Moon?
Express your answer using two significant figures.
To find the diameter of the spot the laser beam will make on the Moon, we can use the formula for the diameter of a spot formed by a diverging laser beam:
diameter = 2 * distance * angle
Given:
distance from Earth to the Moon = 380,000 km = 3.8 x 10^5 km
angle of divergence = 6.2 x 10^(-5) rad
Plugging these values into the formula:
diameter = 2 * (3.8 x 10^5 km) * (6.2 x 10^(-5) rad)
Now we can calculate the result:
diameter = 2 * (3.8 x 10^5 km) * (6.2 x 10^(-5) rad)
= 4 x 10^(-1) km
Expressing the result using two significant figures:
diameter ≈ 0.40 km
To find the diameter of the spot that the laser beam will make on the Moon, we can use the formula for the angular diameter:
Angular diameter = 2 * (tan(angle/2)) * distance
Where:
- Angle is the divergence angle of the laser beam (given as 6.2×10^(-5) rad)
- Distance is the distance from the Earth to the Moon (given as 380,000 km)
First, we need to convert the angle from radians to degrees:
- Angle in degrees = angle in radians * (180/π)
- Angle in degrees = (6.2×10^(-5)) * (180/π)
Next, we need to convert the distance from kilometers to meters:
- Distance in meters = distance in kilometers * 1000
- Distance in meters = 380,000 km * 1000
Now, we can substitute the values into the formula:
Angular diameter = 2 * (tan(angle/2)) * distance
Angular diameter = 2 * (tan((6.2×10^(-5))*(180/π)/2)) * (380,000 km * 1000)
Finally, we can calculate the diameter of the spot by multiplying the angular diameter by the distance to get the actual diameter:
Diameter of the spot = Angular diameter * Distance
Remember to express the answer using two significant figures.
Note: π is a mathematical constant approximately equal to 3.14159.
Please perform the calculations to find the diameter of the spot on the Moon.
multiply them
r = distance = 380,000km
A = angle = 6.2 x 10^-5
The diameter (d) of the spot is given by:
d = r * A
make sure your answer is not supposed to be in meters, if so multiply km by 1000