Question

The phenomenon of diffraction is most significant when the slit width is ________.

• A. much larger than the wavelength
• B. much smaller than the wavelength
• C. comparable to the wavelength
• D. equal to the screen distance
• E. independent of the wavelength

Hint:

This is why we hear sound around corners (large $\lambda$) but don't see light around them (tiny $\lambda$).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Diffraction is the bending or spreading out of waves as they pass through an opening (aperture or slit) or around an obstacle. This question asks for the condition under which this effect is most noticeable or significant.
Step 2: Detailed Explanation
The extent to which a wave diffracts depends on the relative size of the wavelength (\(\lambda\)) of the wave and the size of the opening or obstacle (\(a\)).
- Case 1: Slit width is much larger than the wavelength (\(a \gg \lambda\))
In this case, the waves pass through the opening mostly in a straight line, with very little bending at the edges. The diffraction effect is negligible, and the principles of ray optics (light travels in straight lines) provide a good approximation. We see a sharp shadow.
- Case 2: Slit width is much smaller than the wavelength (\(a \ll \lambda\))
In this case, the slit acts almost like a point source, and the wave spreads out in all directions (hemispherically). While diffraction occurs, the resulting pattern is very spread out and dim, making it hard to observe distinct features like maxima and minima. Also, very little of the wave's energy passes through such a small opening.
- Case 3: Slit width is comparable to the wavelength (\(a \approx \lambda\))
This is the condition where the effects of diffraction are most prominent and easily observable. The wave bends significantly at the edges of the slit, creating a clear and distinct diffraction pattern of bright and dark fringes (maxima and minima). The spreading of the central maximum is substantial. For a single slit, the angular width of the central maximum is given by \(2\theta = 2\sin^{-1}(\lambda/a)\). This width is large and well-defined when \(a \approx \lambda\).
Therefore, diffraction is most significant when the size of the slit is on the same order of magnitude as the wavelength of the wave.
Step 4: Final Answer
The phenomenon of diffraction is most significant when the slit width is comparable to the wavelength.