A laser emits light at a wavelength of 1 = 535.0 nm . The total average power emitted is P =1.50 W .The light is focused down to match the size of a small round spherical perfectly absorbing particle with radius r = 7.00 um . All the light is coming from one direction. The beam of light is a cylinder with r = 7.00 um centered on the particle. 2. %3D a. What is the light intensity near the surface of the particle, I ? b. What force is applied to the particle by radiation pressure, F ? c. If the density of the particle is p= 4.00×10°kg / mʼand the particle is free to move, what is the acceleration of the particle when the laser is turned on, a ?
A laser emits light at a wavelength of 1 = 535.0 nm . The total average power emitted is P =1.50 W .The light is focused down to match the size of a small round spherical perfectly absorbing particle with radius r = 7.00 um . All the light is coming from one direction. The beam of light is a cylinder with r = 7.00 um centered on the particle. 2. %3D a. What is the light intensity near the surface of the particle, I ? b. What force is applied to the particle by radiation pressure, F ? c. If the density of the particle is p= 4.00×10°kg / mʼand the particle is free to move, what is the acceleration of the particle when the laser is turned on, a ?
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![### Laser Emission Analysis for Educational Purposes
2. **Laser Emission and Particle Interaction Analysis**
A laser emits light at a wavelength of \( \lambda = 535.0 \, \text{nm} \). The total average power emitted by the laser is \( P_{\text{av}} = 1.50 \, \text{W} \). This light is meticulously focused to match the size of a small, completely absorbing spherical particle with a radius of \( r = 7.00 \, \mu \text{m} \). All emitted light is directed from one direction only. The beam of light forms a cylinder with a radius \( r = 7.00 \, \mu \text{m} \), centered on the particle.
The following questions explore the interaction between the laser light and the spherical particle:
a. **Light Intensity Near the Surface of the Particle**
- What is the intensity of the light near the surface of the particle, denoted as \( I \)?
b. **Force Applied by Radiation Pressure**
- What is the force applied to the particle due to radiation pressure, denoted as \( F_R \)?
c. **Acceleration of the Particle**
- If the particle's density is \( \rho = 4.00 \times 10^3 \, \text{kg/m}^3 \) and the particle is free to move, what will be the acceleration \( a \) of the particle when the laser is turned on?
### Detailed Explanation:
1. **Calculating the Light Intensity (I)**
- To calculate the light intensity \( I \) near the surface of the particle, we will use the formula for intensity, which is the power per unit area.
\[
I = \frac{P_{\text{av}}}{A}
\]
- Here, \( P_{\text{av}} = 1.50 \, \text{W} \) and the area \( A \) is the cross-sectional area of the laser beam which is \( \pi r^2 \).
\[
A = \pi (7 \times 10^{-6} \, \text{m})^2 = \pi \times 49 \times 10^{-12} \, \text{m}^2 = 1.54 \times 10^{-10} \](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb067f6a6-d6d0-4a81-90c2-26a75bd86046%2F4974edd0-f554-4e07-b681-264e0a36d392%2F32b6npf_processed.png&w=3840&q=75)
Transcribed Image Text:### Laser Emission Analysis for Educational Purposes
2. **Laser Emission and Particle Interaction Analysis**
A laser emits light at a wavelength of \( \lambda = 535.0 \, \text{nm} \). The total average power emitted by the laser is \( P_{\text{av}} = 1.50 \, \text{W} \). This light is meticulously focused to match the size of a small, completely absorbing spherical particle with a radius of \( r = 7.00 \, \mu \text{m} \). All emitted light is directed from one direction only. The beam of light forms a cylinder with a radius \( r = 7.00 \, \mu \text{m} \), centered on the particle.
The following questions explore the interaction between the laser light and the spherical particle:
a. **Light Intensity Near the Surface of the Particle**
- What is the intensity of the light near the surface of the particle, denoted as \( I \)?
b. **Force Applied by Radiation Pressure**
- What is the force applied to the particle due to radiation pressure, denoted as \( F_R \)?
c. **Acceleration of the Particle**
- If the particle's density is \( \rho = 4.00 \times 10^3 \, \text{kg/m}^3 \) and the particle is free to move, what will be the acceleration \( a \) of the particle when the laser is turned on?
### Detailed Explanation:
1. **Calculating the Light Intensity (I)**
- To calculate the light intensity \( I \) near the surface of the particle, we will use the formula for intensity, which is the power per unit area.
\[
I = \frac{P_{\text{av}}}{A}
\]
- Here, \( P_{\text{av}} = 1.50 \, \text{W} \) and the area \( A \) is the cross-sectional area of the laser beam which is \( \pi r^2 \).
\[
A = \pi (7 \times 10^{-6} \, \text{m})^2 = \pi \times 49 \times 10^{-12} \, \text{m}^2 = 1.54 \times 10^{-10} \
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