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.

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.