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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} \
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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