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

Concept: Wavefronts describe the shape of propagating waves. Plane waves have flat wavefronts, while spherical waves have curved wavefronts.
Step 1: Analyze Statement I A prism only refracts light and changes its direction, not the nature of the wavefront. Thus, a plane wave remains a plane wave after passing through a prism. A small pinhole acts like a point source due to diffraction, causing the emerging wavefront to become spherical. \[ \Rightarrow \text{Statement I is true.} \]
Step 2: Analyze Statement II For a slit: - Smaller slit width \(\Rightarrow\) stronger diffraction - Stronger diffraction \(\Rightarrow\) more curvature of wavefront Thus, as slit width increases, diffraction decreases and curvature {decreases}, not increases. \[ \Rightarrow \text{Statement II is false.} \]
Step 3: Final conclusion \[ \text{Statement I is true, Statement II is false.} \]