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  • Interference fringes from sodium light in a double slit experiment ha

Interference fringes from sodium light \mathrm{(1=5890 \AA)} in a double slit experiment have an angular width \mathrm{0.20^{\circ}.} To increase the fringe width by \mathrm{10 \%}, wavelength of light used should be

Option: 1

\mathrm{5892 \AA}


Option: 2

\mathrm{4000 \AA}


Option: 3

\mathrm{8000 \AA}


Option: 4

\mathrm{6479 \AA}


Answers (1)

best_answer

\mathrm{\beta=\frac{\lambda D}{d}} and angular fringe width, \mathrm{\theta=\frac{\beta}{D}=\frac{\lambda}{d}}

\mathrm{ \theta_1=\lambda_1 / \mathrm{d}, \theta_2=\lambda_2 / \mathrm{d} }

\mathrm{ \begin{aligned} & \therefore \frac{\theta_1}{\theta_2}=\frac{\lambda_1}{\lambda_2} \text { or } \lambda_2=\lambda_1 \cdot \frac{\theta_2}{\theta_1} \\\\ & \therefore 5890 \times \frac{0.22}{0.20}=6479 \AA \end{aligned} }

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