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Angular width of a central max. is 300 when the slit is illuminated by light of wavelength 6000 \mathrm{\AA}. Then width of the slit will be approx.

Option: 1

\mathrm{12 \times 10^{-6} \mathrm{~m}}


Option: 2

\mathrm{12 \times 10^{-7} \mathrm{~m}}


Option: 3

\mathrm{12 \times 10^{-8} \mathrm{~m}}


Option: 4

\mathrm{12 \times 10^{-9} \mathrm{~m}}


Answers (1)

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\mathrm{\begin{aligned} & \text { Angular width }=2 \theta=30^{\circ} \\ & \therefore \sin 30^{\circ}=\frac{\lambda}{a} \\ & \therefore \mathrm{a}=\frac{\lambda}{\sin 30^0}=\frac{6000 \times 10^{-10}}{1 / 2}=12000 \times 10^{-10} \mathrm{~m} \\ & =12 \times 10^{-7} \mathrm{~m} \\ & \end{aligned}}

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