91影视

• Intensity of laser beam is$I$.
• Reflecting surface area is.$A$
• The angle between beam and incident beam is.$胃$

By using the concept of the radiation pressure and the ray diagram for the reflection we can find the required expression.

Formulae:

Radiation pressure for the total reflection with the normal incident ray,

$p_r=\frac{F_N}{A}=\frac{2I_N}{C}鈰�鈰�鈰�鈰�鈰�鈰�\left(1\right)$

The trigonometric formula of cosine angle,$\cos \text{鈥�}胃=\frac{\text{adjacentside}}{\text{Hypotenuse}}鈰�鈰�鈰�鈰�鈰�鈰�\left(2\right)$

When the incident ray makes an angle with the surface, then the situation will be as shown.

In$螖ABO$, the angle of$螖ABO$is given using equation (2) as follows:

$\begin{array}{c}\cos \text{鈥�}胃=\frac{F_N}{F_I}\\ F_N=\frac{F_I}{\cos \text{鈥�}胃}鈰�鈰�鈰�鈰�鈰�鈰�\left(3\right)\end{array}$

In,$螖BCO$the angle of $螖BCO$is given using equation (2) as follows:

$\begin{array}{c}\cos \text{鈥�}胃=\frac{I_N}{I}\\ I_N=I\cos \text{鈥�}胃鈰�鈰�鈰�鈰�鈰�鈰�\left(4\right)\end{array}$

Using equations (3) and (4) in equation (1), we can get that

Hence, the expression of radiation of pressure is.$p_r\left(胃\right)=p_{r鈯�}\left({\cos }^2胃\right)$