Новое решение

Alexphysics правка от 29 июн. 2026 г., 05:35

правка #19391 позже →

en/12.1.26.md +26 −0

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		+	### Statement
		+
		+	$12.1.26.$ [Insert the problem statement]
		+
		+	### Solution
		+
		+	The average radiation pressure on a perfect mirror for a sinusoidal plane wave incident at an angle$ \alpha $(measured with respect to the normal) is:
		+
		+	$P = \frac{2I}{c}\cos^2\alpha$
		+
		+	where I is the average intensity of the incident wave. For a plane electromagnetic wave in vacuum
		+
		+	$ I = \dfrac{1}{2}\varepsilon_0 c E_0^2 $
		+
		+	where E_0 is the amplitude of the electric field. Substituting and solving for$ E_0$:
		+
		+	$P = \varepsilon_0 E_0^2 \cos^2\alpha
		+	\quad\Longrightarrow\quad
		+	\boxed{E_0 = \frac{1}{\cos\alpha}\sqrt{\frac{P}{\varepsilon_0}}}$
		+
		+	If the angle were measured with respect to the surface,$ \cos\alpha$ is replaced by$ \sin\alpha$. In the CGS system, the equivalent expression is \displaystyle $E_0 = \frac{\sqrt{4\pi P}}{\cos\alpha}$
		+	(But this is only for knowledge )
		+
		+	#### Answer
		+
		+	[Insert a concise answer or boxed result]

	@@ -0,0 +1,26 @@
			### Statement

			$12.1.26.$ [Insert the problem statement]

			### Solution

			The average radiation pressure on a perfect mirror for a sinusoidal plane wave incident at an angle$ \alpha $(measured with respect to the normal) is:

			$P = \frac{2I}{c}\cos^2\alpha$

			where I is the average intensity of the incident wave. For a plane electromagnetic wave in vacuum

			$ I = \dfrac{1}{2}\varepsilon_0 c E_0^2 $

			where E_0 is the amplitude of the electric field. Substituting and solving for$ E_0$:

			$P = \varepsilon_0 E_0^2 \cos^2\alpha
			\quad\Longrightarrow\quad
			\boxed{E_0 = \frac{1}{\cos\alpha}\sqrt{\frac{P}{\varepsilon_0}}}$

			If the angle were measured with respect to the surface,$ \cos\alpha$ is replaced by$ \sin\alpha$. In the CGS system, the equivalent expression is \displaystyle $E_0 = \frac{\sqrt{4\pi P}}{\cos\alpha}$
			(But this is only for knowledge )

			#### Answer

			[Insert a concise answer or boxed result]