Question

Angular width of central maxima is $\frac{\pi}{2}$. When a slit of width a is illuminated by a light of wavelength 7000Å, then a =

• A. $9\times 10^{-9}m$
• B. \(8.9\times 10^{-7}m\)
• C. \(9\times 10^{-7}m\)
• D. \(9.8\times 10^{-7}m\)

Answer 1

The Correct Option is D

\(a \, \sin \, \theta = n \lambda\)
\(a = \frac{\lambda}{\sin \, \theta} \)
\(ω = 2 \theta\)
\(\theta = \frac{w}{2}=\frac {\pi}{4}\)

\(a=\frac {7000 \times 10^{-10}}{sin \frac \pi4}\)

\(a=\frac {7000 \times 10^{-10}}{\frac {1}{\sqrt 2}}\)
\(a=9.89 \times 10^{-7}\ m\)

So, the correct option is (D): \(9.89 \times 10^{-7}\ m\)