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CBSE Class 12-science Answered

In Young's double slit experiment, the two slits are separated by 0.28mm and the screen is placed at a distance of 1.4m away from the slits. the distance between the centre fringe and the fifth dark fringe is measured to be 1.35cm . calculate the wavelength of light used. Also find the fringe width if the screen is moved 0.4m towards the slits, for the same experiment set up.
Asked by mrwballari999 | 03 Jan, 2023, 09:33: AM
answered-by-expert Expert Answer

Given that,

d = 0.28 x 10-3 m

D = 1.4 m

xn = 1.35 cm x 10-2 m

n = 5

Now, for nth dark fringe we know that,

x subscript n equals fraction numerator left parenthesis 2 n minus 1 right parenthesis over denominator 2 end fraction fraction numerator lambda D over denominator d end fraction
i. e. comma space lambda space equals space fraction numerator 1.35 cross times 10 to the power of negative 2 end exponent cross times 0.28 cross times 10 to the power of negative 3 end exponent cross times 2 over denominator 1.4 cross times 9 end fraction equals 6000 space A

Also when the slit is moved 0.4 m todays the screen the fringe width will be

beta equals fraction numerator lambda D apostrophe over denominator d end fraction equals fraction numerator 6000 cross times 10 to the power of negative 10 end exponent cross times left parenthesis 1.4 minus 0.4 right parenthesis over denominator 0.28 cross times 10 to the power of negative 3 end exponent end fraction equals 0.21 space c m
o r
beta space equals space 2.143 space m m  



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