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  • In a two slit experiment with monochromatic light fringes are obtained on a screen placed at some distance from the sits. If the screen is moved by <img alt="\mathrm{5 \times 10^{-2} \mathrm{~m}}"

In a two slit experiment with monochromatic light fringes are obtained on a screen placed at some distance from the sits. If the screen is moved by \mathrm{5 \times 10^{-2} \mathrm{~m}} towards the slits, the change in fringe width is \mathrm{3 \times 10^{-5} \mathrm{~m}}. If separation between the slits is \mathrm{10^{-3} \mathrm{~m}} , the wavelength of liaht used is

Option: 1

\mathrm{6000 \, \, \AA}


Option: 2

\mathrm{5000\, \, \AA}


Option: 3

\mathrm{\mathrm{3000\, \, \AA}}


Option: 4

\mathrm{\mathrm{4500\, \, \AA}}


Answers (1)

best_answer

\mathrm{\begin{aligned} & \beta=\frac{\lambda D}{d} \Rightarrow \beta \propto D \\\\ & \Rightarrow \frac{\beta_1}{\beta_2}=\frac{D_1}{D_2} \Rightarrow \frac{\beta_1-\beta_2}{\beta_2}=\frac{D_1-D_2}{D_2} \Rightarrow \frac{\Delta \beta}{\Delta D}=\frac{\beta_2}{D_2}=\frac{\lambda_2}{d_2} \\\\ & =\lambda_2=\frac{3 \times 10^{-5}}{5 \times 10^{-2}} \times 10^{-3}=6 \times 10^{-7} \mathrm{~m}=6000 \AA \end{aligned}}

Posted by

Ritika Kankaria

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