Question:
In a Fraunhofer diffraction of a single slit, when a slit is illuminated by a light of wavelength \(6480 \text{Å}\), angular width of central maximum is measured. When the slit is illuminated by light of another wavelength '\(λ\)' the angular width decreases by \(25\%\). The value of \(λ\) in \(\text{Å}\) units is
In a Fraunhofer diffraction of a single slit, when a slit is illuminated by a light of wavelength \(6480 \text{Å}\), angular width of central maximum is measured. When the slit is illuminated by light of another wavelength '\(λ\)' the angular width decreases by \(25\%\). The value of \(λ\) in \(\text{Å}\) units is
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Angular width of the central maximum is 2 lambda over a, so it is proportional to lambda.
Updated On: Oct 1, 2026
- \(4220\)
- \(4530\)
- \(4860\)
- \(5230\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
In single slit diffraction, the angular width of the central maximum is \(2\theta = \frac{2\lambda}{a}\), so for the same slit it is proportional to \(\lambda\).
Step 2: Key Formula or Approach:
A decrease of \(25\%\) means the new width is \(75\%\) of the old width.
Step 3: Detailed Explanation:
\(\lambda' = 0.75\lambda = 0.75 \times 6480 = 4860\ \text{ angstrom}\).
\[ \lambda' = 4860\ \text{ angstrom} \]
The other options give decreases of about \(35\%\), \(30\%\) and \(19\%\), not \(25\%\).
Final Answer:
The wavelength is \(4860\ \text{ angstrom}\), option (C). \[ \boxed{4860\ \text{ angstrom}} \]
In single slit diffraction, the angular width of the central maximum is \(2\theta = \frac{2\lambda}{a}\), so for the same slit it is proportional to \(\lambda\).
Step 2: Key Formula or Approach:
A decrease of \(25\%\) means the new width is \(75\%\) of the old width.
Step 3: Detailed Explanation:
\(\lambda' = 0.75\lambda = 0.75 \times 6480 = 4860\ \text{ angstrom}\).
\[ \lambda' = 4860\ \text{ angstrom} \]
The other options give decreases of about \(35\%\), \(30\%\) and \(19\%\), not \(25\%\).
Final Answer:
The wavelength is \(4860\ \text{ angstrom}\), option (C). \[ \boxed{4860\ \text{ angstrom}} \]
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