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NEET Sample Paper NEET Sample Test Paper-80

  • question_answer
    White light is used to illuminate the two slits in a Young?s double slit experiment. The separation between slits is b and the screen is at a distance \[d(>>b)\] from the slits. At a point on the screen directly in front of one the slits, certain wavelengths are missing. One of the missing wavelengths is

    A)  \[\lambda ={{b}^{2}}/d\]                   

    B)  \[\lambda =2\,\,{{b}^{2}}/d\]

    C)  \[\lambda =3\,\,{{b}^{2}}/d\]             

    D)  \[\lambda =2\,\,{{b}^{2}}/3d\]

    Correct Answer: A

    Solution :

    Positions of minima are given by \[{{y}_{n}}=\left( n-\frac{1}{2} \right)\,\,\frac{D\,\lambda }{d}\] \[\lambda \,\,=\,\,\frac{2\,\,{{y}_{n}}\,d}{(2\,n\,-1)\,D}\] Here, \[{{\operatorname{y}}_{n}}\,\,=\,\,b/2,\,\,d=b,\,\,D=d\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\lambda =\frac{{{b}^{2}}}{(2n-1)d}\] where \[\operatorname{n}\,\,=\,\,1, 2,\,\,3,....\] Hence, \[\lambda =\frac{{{b}^{2}}}{d},\,\,\,\frac{{{b}^{2}}}{3\,d},\,\,....\]


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