# Radiation force on a solid hemisphere

• Krushnaraj Pandya
In summary, the question asks for the force exerted by a parallel beam of light on a perfectly reflecting solid hemisphere of radius R. The equation for radiation pressure is given, where I is intensity, po is reflection coefficient, x is angle of incidence, and c is the speed of light. It is noted that the force will be less than on a disc of the same radius and that integration will be involved in the solution. The relevance of the impulse applied by a photon and the consideration of an element of the hemisphere where this component is approximately constant is also mentioned.
Krushnaraj Pandya
Gold Member

## Homework Statement

A perfectly reflecting solid hemisphere of radius R is placed in the path of a parallel beam of light of large aperture, if the beam carries an intensity I, what is the force exerted by the beam on the hemisphere?

## Homework Equations

I is intensity, po is reflection coefficient, x is angle of incidence and c is speed of light.

## The Attempt at a Solution

ro=1 here, Intuitively the force will be less than on a disc of the same radius, so it is less than 2*pi*r*r*I/c, I also know integration will be involved but I can't figure out how to go about it. I'd appreciate some help, thank you

Krushnaraj Pandya said:
integration will be involved
For any particular photon, what component of the impulse it applies is relevant?
Consider an element of the hemisphere over which that component is approximately constant.

## 1. What is radiation force on a solid hemisphere?

Radiation force on a solid hemisphere is the force exerted by electromagnetic radiation on a solid hemisphere. This force is caused by the transfer of momentum from the radiation to the solid surface.

## 2. How is radiation force on a solid hemisphere calculated?

The radiation force on a solid hemisphere can be calculated by using the formula F = P/c, where F is the force, P is the radiation pressure, and c is the speed of light. The radiation pressure can be calculated using the formula P = I/c, where I is the intensity of the radiation.

## 3. What factors affect the radiation force on a solid hemisphere?

The radiation force on a solid hemisphere is affected by the intensity and wavelength of the radiation, the size and shape of the hemisphere, and the material properties of the hemisphere. The angle of incidence of the radiation also plays a role in determining the force.

## 4. How does the angle of incidence affect the radiation force on a solid hemisphere?

The angle of incidence of the radiation affects the radiation force on a solid hemisphere in that the force is strongest when the radiation is incident perpendicular to the surface of the hemisphere. As the angle of incidence increases, the force decreases.

## 5. What are some practical applications of radiation force on a solid hemisphere?

Radiation force on a solid hemisphere has various practical applications, including in optical trapping and manipulation, particle separation and sorting, and in controlling the motion of small particles or droplets in microfluidic devices. It is also utilized in the study of the effects of radiation on materials and in the development of new technologies such as solar sails.

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