Question:
A slit of width \(a\) is illuminated by light of wavelength \(\lambda\). The linear separation between 1st and 3rd minima in the diffraction pattern produced on a screen placed at a distance \(D\) from the slit system is ______.
A slit of width \(a\) is illuminated by light of wavelength \(\lambda\). The linear separation between 1st and 3rd minima in the diffraction pattern produced on a screen placed at a distance \(D\) from the slit system is ______.
Updated On: Apr 10, 2026
- \(\frac{D\lambda}{a}\)
- \(1.5 \frac{D\lambda}{a}\)
- \(\frac{2D\lambda}{a}\)
- \(\frac{3D\lambda}{a}\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
In Fraunhofer diffraction by a single slit, the position of the \(n^{th}\) minimum on the screen is given by the condition \(a \sin \theta = n\lambda\). For small angles, the linear distance from the central maximum is \(y_n = \frac{n D \lambda}{a}\).
Step 2: Key Formula or Approach:
1. Linear position of \(n^{th}\) minimum: \(y_n = n \left( \frac{D\lambda}{a} \right)\). 2. Linear separation \(\Delta y = y_3 - y_1\).
Step 3: Detailed Explanation:
1. Position of the 1st minimum (\(n=1\)): \[ y_1 = 1 \cdot \frac{D\lambda}{a} \] 2. Position of the 3rd minimum (\(n=3\)): \[ y_3 = 3 \cdot \frac{D\lambda}{a} \] 3. Linear separation: \[ \Delta y = y_3 - y_1 = (3 - 1) \frac{D\lambda}{a} = \frac{2D\lambda}{a} \]
Step 4: Final Answer:
The linear separation is \(\frac{2D\lambda}{a}\).
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