Question 143: Wave Optics

Question

Consider a Young’s double slit experiment as shown in figure. What should be the slit separation d in terms of wavelength $\lambda $ such that the first minima occurs directly in front of the slit (S
1
) ?
![](https://imagex.cdn.examgoal.net/RZL8veNk7tnrKPRIa/gGn64PszzsX9ysPhcdnGdbgUxbf7v/2Ahbt2DZqiJkoV9ZM4a58r/image.png)

Accepted Answer

Path difference, S
2
P Ã¢ÂÂ S
1
P = ${\lambda  \over 2}$
$ \Rightarrow $ $\sqrt {4{d^2} + {d^2}}  - 2d = {\lambda  \over 2}$
$ \Rightarrow $ $d\left( {\sqrt 5  - 2} \right) = {\lambda  \over 2}$
$ \Rightarrow $ d = ${\lambda  \over {2\left( {\sqrt 5  - 2} \right)}}$

Answer

${\lambda  \over {2\left( {5 - \sqrt 2 } \right)}}$

Answer

${\lambda  \over {2\left( {\sqrt 5  - 2} \right)}}$

Answer

${\lambda  \over {\left( {5 - \sqrt 2 } \right)}}$

Answer

${\lambda  \over {\left( {\sqrt 5  - 2} \right)}}$

Wave Optics

Consider a Young’s double slit experiment as shown in figure. What should be the slit separation d in terms of wavelength \lambda such that the first minima occurs directly in front of the slit (S 1 ) ?

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