91Ó°ÊÓ

The concept of light intensity is pivotal when discussing laser beams and their effects. Intensity refers to the amount of energy a light beam carries in a given area per second. It's measured in watts per square meter (\(\text{W/m}^2\)).
To find the intensity of a light beam, such as from a laser, you use the formula: \(I = \frac{P}{A}\), where \(P\) is the power of the laser and \(A\) is the area over which the power is spread. For Example:
- Calculate the area \(A\) of the beam: the area of a circle (since the beam is usually circular) is \(A = \pi\left(\frac{d}{2}\right)^2\), with \(d\) being the diameter.
- This means if a laser has a power output of 5 mW (milliwatts) and a beam diameter of 1206 nm, you can determine its intensity.
- The area would be \(A \approx 1.14 \times 10^{-12} \text{ m}^2\) and thus, the intensity \(I \approx 4.39 \times 10^9 \text{ W/m}^2\).
Understanding intensity is crucial as it affects how much pressure and force the light exerts on objects. The stronger the intensity, the more substantial its impacts.

Calculating the force due to light on a surface involves understanding radiation pressure. Radiation pressure is the pressure exerted by light when it hits a surface.
For a perfectly absorbing object like our sphere, the radiation pressure \(P_r\) can be calculated by dividing the light's intensity by the speed of light \(c\): \(P_r = \frac{I}{c}\).
Here’s how it works:
- With intensity \(I = 4.39 \times 10^9 \text{ W/m}^2\) and \(c = 3.00 \times 10^8 \text{ m/s}\), we find \(P_r \approx 14.6 \text{ Pa}\) (pascals).
- The force (\(F\)) exerted by this pressure on the sphere is found by multiplying the pressure by the area it affects: \(F = P_r \times A\).
- Using our previously calculated area \(A \approx 1.14 \times 10^{-12} \text{ m}^2\), the force \(F \approx 1.66 \times 10^{-11} \text{ N}\).
Therefore, this calculation is essential for understanding how light can influence motion and behavior in microscopic systems.

Acceleration due to light pressure is an intriguing demonstration of how light, a seemingly intangible phenomenon, can produce physical movement. This effect follows from Newton's second law of motion.
Here’s the approach:
- First, determine the mass \(m\) of the sphere, which involves calculating its volume and using its density: 1. Volume \(V = \frac{4}{3}\pi\left(\frac{d}{2}\right)^3\) for our sphere results in \(V \approx 9.18 \times 10^{-22} \text{ m}^3\). 2. With a density of \(5.00 \times 10^{3} \text{ kg/m}^{3}\), the mass is \(m \approx 4.59 \times 10^{-18} \text{ kg}\).
- Then, utilize the force calculated earlier \(F \approx 1.66 \times 10^{-11} \text{ N}\) and apply Newton’s formula \(a = \frac{F}{m}\) to find acceleration.
- This gives an acceleration \(a \approx 3.62 \times 10^6 \text{ m/s}^2\).
Understanding acceleration due to light pressure is particularly important in fields like space technology, where light-powered propulsion is a potential area of exploration.