Question

A hollow circular pipe with non-reflective inner surface is cut into 5 pieces and arranged as shown in the figure below. If it is illuminated from below using a torch as shown in the figure, what would be the profile of the light falling on the sheet kept above? 

• A. A
• B. B
• C. C
• D. D

Hint:

In problems involving light and apertures, always remember that light travels in straight lines. Trace the "lines of sight" from the edges of the light source through the edges of the apertures to determine the shape of the resulting pattern.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept: 
This question tests understanding of basic optics, specifically the principle that light travels in straight lines. We need to determine the shape of the light that passes through a series of misaligned circular apertures. 

Step 2: Detailed Explanation: 
Light Path: The torch at the bottom emits light rays in all upward directions. However, only the rays that can travel in a straight line from the torch, through all five staggered pipe sections, will reach the sheet at the top. 
Aperture Effect: Each piece of pipe acts as a circular aperture (opening). Because these apertures are not perfectly aligned, they collectively form a constricted, offset "tunnel" for the light. 
Shape Formation: The final shape of the light on the sheet is the projection of the first (bottom) aperture onto the plane of the last (top) aperture, as viewed through the intermediate apertures. Since the pipes are staggered horizontally, the light path will be elongated in the direction of the stagger. The top and bottom of the shape will be curved, defined by the circular edges of the pipe openings. The resulting shape is an elongated oval, or an ellipse. The inner surface is non-reflective, so we don't need to consider any bounced light. 

Step 3: Analyzing the Options: 
(A): This shows an elongated, smooth oval shape. This correctly represents the profile created by light passing through a series of staggered circular apertures. 
(B): This shape has an indentation in the middle. The setup would not create such a blockage; the overlapping circles would form a continuous, convex shape. 
(C): This is a less elongated oval. Given the significant stagger shown in the diagram, the light profile would be more stretched out than this. 
(D): This shows a straight vertical line. This would only be possible if the light source was a single point and the pipes were cut into thin slits, not circular sections. 

Step 4: Final Answer: 
The light passing through the staggered pipe sections will form an elongated oval shape. Option (A) is the most accurate representation of this profile.