A diffraction pattern is obtained using a beam of red light. What happens if the red light is replaced by blue light?

  • No change
  • Diffraction bands become narrower and crowded together
  • Bands become broader and farther apart
  • Bands disappear.

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When a diffraction pattern is generated using red light and then the red light is replaced by blue light, the nature of the bands changes. This change can be understood by considering the relationship between wavelength and diffraction fringe width.

  1. Wavelength Comparison:

    • The wavelength of red light ($ \lambda_{red} $) is greater than the wavelength of blue light ($ \lambda_{blue} $).
  2. Fringe Width Calculation: The width of the diffraction bands, often denoted as $ \beta $, is given by the formula: $$ \beta = \frac{D \lambda}{d} $$ where:

    • $ D $ = Distance from the slit to the screen
    • $ \lambda $ = Wavelength of the light
    • $ d $ = Width of the slit
  3. Proportional Relationship:

    • Since $ D $ and $ d $ remain constant, $\beta$ is directly proportional to $\lambda$: $$ \beta \propto \lambda $$
  4. Effect on Diffraction Pattern:

    • When red light (larger $ \lambda $) is replaced with blue light (smaller $ \lambda $), $$ \beta_{blue} < \beta_{red} $$
    • Therefore, the diffraction bands with blue light will become narrower and will be closer together.

Conclusion: Replacing red light with blue light in a diffraction experiment will lead to diffraction bands becoming narrower and crowded together.

Thus, the correct answer is B. Diffraction bands become narrower and crowded together.

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