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CBSE Class 12-science Answered

In a double slit experiment , a dichromatic light of wavelength 6500 A° and 5200 A°  are used. What is the minimum distance from the central bright band at where the bright  band of each of the colours will superpower? Given distance between two slits is (2×10^-3)m and distance between slits and screen is 1.2 m.
Asked by mridulabarua05 | 19 Feb, 2019, 11:54: AM
answered-by-expert Expert Answer
Distance of nth bright fringe from centre = begin mathsize 12px style n fraction numerator lambda D over denominator d end fraction end style, where λ is wavelength of light used, D is slit-to-screen distance and d is distance between slits.
if nth bright fringe of light of wavelength 6500 Aº coincides with the mth bright fringe of wavelength 5200 Aº, then we have
 
begin mathsize 12px style n cross times fraction numerator 6500 cross times 10 to the power of negative 8 end exponent cross times 1.2 over denominator 2 cross times 10 to the power of negative 3 end exponent end fraction space equals space m cross times fraction numerator 5200 cross times 10 to the power of negative 8 end exponent cross times 1.2 over denominator 2 cross times 10 to the power of negative 3 end exponent end fraction space space.................... left parenthesis 1 right parenthesis
end style
To have mimimum distance where bright fringes of both lights superimpose, we need to find mimimum numbers of n and m so that
the products (n×65)  and (m×52) are equal.  This is true if n = 4 and m = 5
 
hence minimum distance is       begin mathsize 12px style 4 cross times fraction numerator 6500 cross times 10 to the power of negative 8 end exponent cross times 1.2 over denominator 2 cross times 10 to the power of negative 3 end exponent end fraction space equals space 0.156 space m
end style  
Answered by Thiyagarajan K | 19 Feb, 2019, 02:20: PM
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