Question

Given below are two statements: Statement I: A plane wave after passing through a prism remains a plane wave, but passing through a small pin hole may become a spherical wave. Statement II: The curvature of a spherical wave emerging from a slit will increase for increasing slit width. In the light of the above statements, choose the correct answer:

• A. Both Statement I and Statement II are false
• B. Both Statement I and Statement II are true
• C. Statement I is false but Statement II is true
• D. Statement I is true but Statement II is false

Hint:

Diffraction effects are stronger when the aperture size is comparable to the wavelength.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This question explores the nature of wavefronts and how they transform when passing through optical elements or apertures (Huygens' Principle and Diffraction).
Step 2: Detailed Explanation:
Statement I Analysis:
A prism shifts the direction of a plane wave but does not alter the relative phase of the parallel rays, so the wavefront remains planar.
According to Huygens' Principle, a very small pinhole acts as a secondary point source, which generates spherical waves in all forward directions. Thus, Statement I is True.
Statement II Analysis:
Curvature is defined as \(1/R\), where \(R\) is the radius of the wavefront.
As the slit width increases, the diffraction effect decreases. The central part of the emerging wave becomes "flatter", resembling a plane wave.
For a plane wave, \(R \to \infty\), which means curvature (\(1/R\)) tends to zero.
Therefore, increasing the slit width decreases the curvature of the emerging wavefront. Thus, Statement II is False.
Step 3: Final Answer:
Statement I is true but Statement II is false.