Question

A parallel beam of monochromatic light of wavelength $5\times10^{-7\,\text{m}$ is incident normally on a single narrow slit of width $10^{-3}\,\text{mm}$. At what angle of diffraction, the first minima is observed?}

• A. $\sin^{-1}\left(\dfrac{1}{\sqrt{2}}\right)$
• B. $\sin^{-1}(1)$
• C. $\sin^{-1}\left(\dfrac{\sqrt{3}}{2}\right)$
• D. $\sin^{-1}\left(\dfrac{1}{2}\right)$

Hint:

For single slit diffraction, first minima occurs when slit width equals one wavelength path difference.

Answer 1

The Correct Option is D

Step 1: Condition for first minima in single slit diffraction.
\[ a\sin\theta = \lambda \]
Step 2: Substituting given values.
\[ a = 10^{-3}\,\text{mm} = 10^{-6}\,\text{m}, \quad \lambda = 5\times10^{-7}\,\text{m} \]
Step 3: Calculating $\sin\theta$.
\[ \sin\theta = \frac{\lambda}{a} = \frac{5\times10^{-7}}{10^{-6}} = \frac{1}{2} \]
Step 4: Conclusion.
\[ \theta = \sin^{-1}\left(\frac{1}{2}\right) \]