In a Fraunhofer diffraction at a single slit, if yellow light illuminating the slit is replaced by blue light, then diffraction bands

Options

A. Remain unchanged
B. Become wider
C. Disappear
D. Become narrower

Answer

To solve the problem regarding the effect of replacing yellow light with blue light in a Fraunhofer diffraction experiment at a single slit, we need to analyze how the wavelength of light affects the diffraction pattern.

### Step-by-Step Solution:

1. **Understanding Wavelengths**:
- Yellow light has a longer wavelength compared to blue light. For example, the wavelength of yellow light is approximately 580 nm, while blue light has a wavelength around 450 nm.

2. **Diffraction Condition**:
- The condition for minima in a single slit diffraction pattern is given by the formula:
\[ a \sin \theta = n \lambda \]
where \( a \) is the slit width, \( \theta \) is the angle of diffraction, \( n \) is the order of the minima, and \( \lambda \) is the wavelength of the light used.

3. **Effect of Wavelength on Angular Width**:
- The angular width of the central maximum is determined by the first minimum on either side of the central maximum, which can be approximated as:
\[ \theta \approx \frac{\lambda}{a} \]
- Therefore, the width of the central maximum is approximately:
\[ \text{Width} \approx 2\theta \approx \frac{2\lambda}{a} \]

4. **Comparing Yellow and Blue Light**:
- Since blue light has a shorter wavelength than yellow light, substituting blue light into the equation will result in a smaller value for \( \lambda \).
- Consequently, the width of the central maximum will decrease when blue light is used instead of yellow light.

5. **Conclusion**:
- Thus, when yellow light is replaced by blue light in a Fraunhofer diffraction experiment at a single slit, the diffraction bands will become narrower due to the shorter wavelength of blue light.

### Final Answer:
The diffraction bands will become narrower when yellow light is replaced by blue light.

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