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Question

Physics Question on Wave optics

Angular width of central maxima is π2\frac{\pi}{2}. When a slit of width a is illuminated by a light of wavelength 7000Å, then a =

A

9×10−9m9\times 10^{-9}m

B

8.9×10−7m8.9\times 10^{-7}m

C

9×10−7m9\times 10^{-7}m

D

9.8×10−7m9.8\times 10^{-7}m

Answer

9.8×10−7m9.8\times 10^{-7}m

Explanation

Solution

a sin⁡ θ=nλa \, \sin \, \theta = n \lambda
a=λsin⁡ θa = \frac{\lambda}{\sin \, \theta}
ω=2θω = 2 \theta
θ=w2=π4\theta = \frac{w}{2}=\frac {\pi}{4}

a=7000×10−10sinπ4a=\frac {7000 \times 10^{-10}}{sin \frac \pi4}

a=7000×10−1012a=\frac {7000 \times 10^{-10}}{\frac {1}{\sqrt 2}}
a=9.89×10−7 ma=9.89 \times 10^{-7}\ m

So, the correct option is (D): 9.89×10−7 m9.89 \times 10^{-7}\ m