In a single slit diffraction, first minimum for green light of wavelength 5240 A ˙ coincides with first maximum of some other wavelength λ 1 '. Find the value of λ 1 .

Question

In a single slit diffraction, first minimum for green light of wavelength   5240               A      ˙       coincides with first maximum of some other wavelength       λ    1  &#039;. Find the value of       λ    1  .

Kaiden Weeks · Accepted Answer

Since, Between the first and second minima, there is a maxima of undetermined wavelength.And,Position of minima in diffraction Pattern is   n  λ  =  d  sin  ⁡  θThus, For first minima of Green Light of wavelength       λ    g   will be,  n      λ    g    =  d  sin  ⁡      θ    1  To Calculate The first maxima of some other wavelength       λ    1   will be at position,      3    2        λ    1    =  d  sin  ⁡      θ    2  For the first minimum of diffraction Pattern of Green light  n      λ    g    =  d  sin  ⁡      θ    1  For the first maxima of some other light of wavelength       λ    1        3    2        λ    1    =  d  sin  ⁡      θ    2  Since, first minimum of green light coincide with the first maximum of the other light therefore,      θ    1    =      θ    2      thus    sin  ⁡      θ    1    =  sin  ⁡      θ    2  Therefore we can write it as,      3    2        λ    1    =  n      λ    g  Given:n=1 (for first minima)      λ    g    =  5240               A      ˙              3    2        λ    1    =  1  (  5240            A      ˙        )        λ    1    =            2      ×      5240                        A          ˙                      3          λ    1    =  3493            A      ˙      The Wavelength of the first maxima of some other light is        λ    1    =  3493            A      ˙

Find the value of lambda_2.

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