Final answer:
The radiation pressure exerted on a perfectly reflecting mirror by a 27.3-mW laser beam with a diameter of 1.91 mm is approximately 6.35×10⁻⁵ pascals.
Step-by-step explanation:
To calculate the radiation pressure exerted on a mirror by a laser beam, we can use the formula for pressure P when light is reflected with no absorption:
P = 2I/c
where I is the intensity of the laser beam (power per unit area) and c is the speed of light in vacuum.
The intensity I can be found by dividing the power of the laser by the area of the beam's cross-section.
I = power / area
The area of the laser beam's cross-section, assuming it's circular, is A = πd²/4, where d is the diameter of the beam.
For a 27.3-mW laser with a diameter of 1.91 mm, the calculations will be as follows:
- First, convert the power from milliwatts to watts: 27.3 mW = 0.0273 W.
- Next, find the area using the diameter in meters (1.91 mm = 0.00191 m):
A = π(0.00191 m)²/4 ≈ 2.865×10⁻⁶ m² - Now, calculate the intensity:
I = 0.0273 W / 2.865×10⁻⁶ m² ≈ 9.53×10³ W/m² - Finally, calculate the radiation pressure using the speed of light (c ≈ 3×10⁸ m/s):
P = 2 × 9.53×10³ W/m² / 3×10⁸ m/s ≈ 6.35×10⁻⁵ Pa
The radiation pressure on the mirror is approximately 6.35×10⁻⁵ Pa.