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  • Laser light of wavelength incident on a pair of slits produce

Laser light of wavelength \mathrm{630 \mathrm{~nm}} incident on a pair of slits produces an interference pattern in which the bright fringes are separated by \mathrm{8.1 \mathrm{~mm}}. A second light produces an interference pattern in which the fringes are separated by \mathrm{7.2 \mathrm{~mm}}. The wavelength of the second light is:

Option: 1

420 nm


Option: 2

560 nm


Option: 3

810 nm


Option: 4

980 nm


Answers (1)

best_answer

Here, \mathrm{ \lambda_1=630 \mathrm{~nm}, \beta_1=8.1 \mathrm{~mm}, \beta_2=7.2 \mathrm{~mm}}

Fringe width, \mathrm{ \beta=\frac{D \lambda}{d}}

For constant \mathrm{\mathrm{D}} and \mathrm{\mathrm{d}, \beta \propto \lambda}

\mathrm{ \begin{aligned} & \therefore \frac{\beta_2}{\beta_1}=\frac{\lambda_2}{\lambda_1} \\ & \therefore \quad \lambda_2=\frac{\beta_2}{\beta_1} \times \lambda_1=\frac{7.2 \mathrm{~mm}}{8.1 \mathrm{~mm}} \times 630 \mathrm{~nm}=560 \mathrm{~nm} \end{aligned} }

Posted by

himanshu.meshram

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