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Find the order of the fringe formed at O.
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Answer
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Hint: First calculate the path difference at O. The path difference here is the difference between the SS2&SS1since, the distances S1O&S2O are equal. Then calculate the thickness, t. Also path difference is the product of its wavelength and order of the fringe. Thus by rearranging the equation and substituting the values of wavelength and path difference we will get the order of the fringe.

Complete answer:
The path difference is denoted by the letter x .
Hence,
x=(SS2+S2O)(SS1+S1O)x=SS2SS1
That is, the distances S1O&S2O are equal.
Then thickness t is,
t=22+1.52=2.5mm
Then,
x=μttx=(65×2.5)2.5x=0.5mm
The path length difference must be an integral multiple of the wavelength.
So, x=nλ
n=xλ
Substituting the value we get,
n=0.5×103500×109n=1000

Additional information:
(2n1)λ1D2d=(2m1)λ2D2d
where, d is the distance between the slits.
D, the distance between the slit and screen.
λ1&λ2 are the wavelengths of light used.
m and n are the order of interference.
 To obtain constructive interference for a double slit, the path length difference must be an integral multiple of the wavelength.
dsinθ=mλ
 For m= 0,1,-1,2,-2,…… (Constructive interference)
dsinθ=(m+12)λ
For m=0,1,-1,2,-2,……….(Destructive interference)
Here, λ is the wavelength of light, d is the distance between the slits and m is the order of interference.

Note:
The value of m and n should not be a decimal or a fractional number. The path difference here is the difference between the SS2 andSS1 since, the distances S1O&S2O are equal. Also path difference is the product of its wavelength and order of the fringe. To obtain constructive interference for a double slit, the path length difference must be an integral multiple of the wavelength.