Question:
A monochromatic light is incident on a single slit of width 0.014 mm. The angular position of the second bright line observed is \(2.81^\circ\). Find the wavelength of the incident light. \([ \sin(2.81^\circ) = 0.049072 ]\)
A monochromatic light is incident on a single slit of width 0.014 mm. The angular position of the second bright line observed is \(2.81^\circ\). Find the wavelength of the incident light. \([ \sin(2.81^\circ) = 0.049072 ]\)
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Single-slit bright fringe approximate: \(\lambda = \frac{a \sin \theta}{m}\). Convert slit width to meters, angle in radians or use sine.
Updated On: Jul 18, 2026
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- 2748
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The Correct Option is D
Solution and Explanation
Step 1: Recall single-slit diffraction formula.
Position of bright fringes (m-th bright) approximately:
\[ a \sin \theta = m \lambda \]
where \(a = 0.014 \, \text{mm} = 1.4 \times 10^{-5} \, \text{m}\), \(\theta = 2.81^\circ\), \(m = 2\).
Step 2: Solve for wavelength.
\[ \lambda = \frac{a \sin \theta}{m} = \frac{1.4 \times 10^{-5} \cdot 0.049072}{2} \]
Step 3: Compute product.
\[ 1.4 \times 10^{-5} \cdot 0.049072 \approx 6.870 \times 10^{-7} \, \text{m} \]
Step 4: Divide by m = 2.
\[ \lambda = \frac{6.87 \times 10^{-7}}{2} \approx 3.435 \times 10^{-7} \, \text{m} \approx 2748 \, \text{\AA} \]
Step 5: Verify order of magnitude.
Visible light wavelength consistent, ~2748 Å (UV range).
Step 6: Final conclusion.
\[ \boxed{2748 \, \text{\AA}} \]
Position of bright fringes (m-th bright) approximately:
\[ a \sin \theta = m \lambda \]
where \(a = 0.014 \, \text{mm} = 1.4 \times 10^{-5} \, \text{m}\), \(\theta = 2.81^\circ\), \(m = 2\).
Step 2: Solve for wavelength.
\[ \lambda = \frac{a \sin \theta}{m} = \frac{1.4 \times 10^{-5} \cdot 0.049072}{2} \]
Step 3: Compute product.
\[ 1.4 \times 10^{-5} \cdot 0.049072 \approx 6.870 \times 10^{-7} \, \text{m} \]
Step 4: Divide by m = 2.
\[ \lambda = \frac{6.87 \times 10^{-7}}{2} \approx 3.435 \times 10^{-7} \, \text{m} \approx 2748 \, \text{\AA} \]
Step 5: Verify order of magnitude.
Visible light wavelength consistent, ~2748 Å (UV range).
Step 6: Final conclusion.
\[ \boxed{2748 \, \text{\AA}} \]
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