A parallel beam of light of wavelength 500 nm is incident normally on a single slit of width \( 10^{-6}\,\mathrm{m} \). The light is focused by a convex lens on a screen placed in focal plane. What is the angle of diffraction for the first minimum formed?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 30^\circ \)
In single-slit diffraction the first minimum lies in the direction where the path difference between the two edges of the slit is one wavelength.
\( \displaystyle a\sin\theta = \lambda \;\Rightarrow\; \sin\theta = \frac{\lambda}{a} \)
\( \lambda = 500\,\mathrm{nm} = 5\times10^{-7}\,\mathrm{m} \)
\( a = 10^{-6}\,\mathrm{m} \)
\( \displaystyle \sin\theta = \frac{5\times10^{-7}\,\mathrm{m}}{10^{-6}\,\mathrm{m}} = 0.5 \)
\( \theta = 30^\circ \)
The convex lens only brings the parallel diffracted rays to a focus on the screen; it does not change the angle of diffraction.