Edits to “Statement”, “Solution”, “Answer”

Valter edited Aug 22, 2026, 12:50 PM

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revision #20226 parent #20225 ← older

en/13.1.11.md +2 −10

		@@ -1,11 +1,5 @@
			### Statement

		−	$13.1.11.$ [Insert the problem statement]
		−
		−	### Solution
		−
		−	### Statement
		−
			$13.1.11.$ If a tube with a smooth inner surface is placed between a point source and a screen, a system of concentric rings will appear on the screen. Explain the reason for their appearance.

			### Solution

			The appearance of the system of concentric rings is explained by the laws of geometric optics (multiple reflections), not by interference.

			Light from the point source spreads in all directions. Some of the rays pass through the tube directly, illuminating the central spot on the screen. The remaining rays fall on the smooth inner walls of the tube at various angles and undergo reflections.
			Due to the cylindrical symmetry of the tube, a group of rays that has undergone exactly one reflection from the walls ($n=1$) exits the tube as a hollow conical beam. When this cone intersects the flat screen, the first bright light ring is formed.

		@@ -18,9 +12,7 @@Solution
			Rays falling on the walls at slightly larger angles will undergo exactly two reflections inside the tube ($n=2$). They will exit the tube as a cone with a different aperture angle and form a second ring of a larger radius on the screen.
			Since the number of reflections a ray undergoes from the tube walls can only take integer discrete values ($n = 1, 2, 3 \dots$), a strict system of discrete concentric rings is formed on the screen rather than continuous illumination.

		−	#### Answer
		−	The rings appear due to the multiple reflections of light from the cylindrical walls of the tube. Each ring is formed by a beam of rays that have undergone a strictly defined integer number of reflections ($1, 2, 3 \dots$).
		+	(For more details on this optical phenomenon, see: [Reflections in a Polished Tube](https://cupola.gettysburg.edu/cgi/viewcontent.cgi?article=1083&context=physfac))

			#### Answer
		−
		−	[Insert a concise answer or boxed result]
		+	The rings appear due to the multiple reflections of light from the cylindrical walls of the tube. Each ring is formed by a beam of rays that have undergone a strictly defined integer number of reflections ($1, 2, 3 \dots$).

	@@ -1,11 +1,5 @@
	### Statement		### Statement

	$13.1.11.$ [Insert the problem statement]

	### Solution

	### Statement

	$13.1.11.$ If a tube with a smooth inner surface is placed between a point source and a screen, a system of concentric rings will appear on the screen. Explain the reason for their appearance.		$13.1.11.$ If a tube with a smooth inner surface is placed between a point source and a screen, a system of concentric rings will appear on the screen. Explain the reason for their appearance.

	### Solution		### Solution

	The appearance of the system of concentric rings is explained by the laws of geometric optics (multiple reflections), not by interference.		The appearance of the system of concentric rings is explained by the laws of geometric optics (multiple reflections), not by interference.

	Light from the point source spreads in all directions. Some of the rays pass through the tube directly, illuminating the central spot on the screen. The remaining rays fall on the smooth inner walls of the tube at various angles and undergo reflections.		Light from the point source spreads in all directions. Some of the rays pass through the tube directly, illuminating the central spot on the screen. The remaining rays fall on the smooth inner walls of the tube at various angles and undergo reflections.
	Due to the cylindrical symmetry of the tube, a group of rays that has undergone exactly one reflection from the walls ($n=1$) exits the tube as a hollow conical beam. When this cone intersects the flat screen, the first bright light ring is formed.		Due to the cylindrical symmetry of the tube, a group of rays that has undergone exactly one reflection from the walls ($n=1$) exits the tube as a hollow conical beam. When this cone intersects the flat screen, the first bright light ring is formed.

	@@ -18,9 +12,7 @@Solution
	Rays falling on the walls at slightly larger angles will undergo exactly two reflections inside the tube ($n=2$). They will exit the tube as a cone with a different aperture angle and form a second ring of a larger radius on the screen.		Rays falling on the walls at slightly larger angles will undergo exactly two reflections inside the tube ($n=2$). They will exit the tube as a cone with a different aperture angle and form a second ring of a larger radius on the screen.
	Since the number of reflections a ray undergoes from the tube walls can only take integer discrete values ($n = 1, 2, 3 \dots$), a strict system of discrete concentric rings is formed on the screen rather than continuous illumination.		Since the number of reflections a ray undergoes from the tube walls can only take integer discrete values ($n = 1, 2, 3 \dots$), a strict system of discrete concentric rings is formed on the screen rather than continuous illumination.

	#### Answer		(For more details on this optical phenomenon, see: [Reflections in a Polished Tube](https://cupola.gettysburg.edu/cgi/viewcontent.cgi?article=1083&context=physfac))
	The rings appear due to the multiple reflections of light from the cylindrical walls of the tube. Each ring is formed by a beam of rays that have undergone a strictly defined integer number of reflections ($1, 2, 3 \dots$).

	#### Answer		#### Answer
			The rings appear due to the multiple reflections of light from the cylindrical walls of the tube. Each ring is formed by a beam of rays that have undergone a strictly defined integer number of reflections ($1, 2, 3 \dots$).
	[Insert a concise answer or boxed result]