Question

# In Young's double slit experiment, the slits are 2mm apart are illuminated by photons of two wavelengths I1=12000藲A and I2=10000藲A. at what minimum distance from the common central bright fringe on the screen 2m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?

A
8 mm
B
6 mm
C
4 mm
D
3 mm
Solution
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#### The correct option is B 6 mmNow, from the question we can infer thatn1λ1=n2λ2so,n1n2=λ2λ1or n1n2=10000A12000Athus,we haven1n2=565th and 6th fringes will coincide respectively.the minimum distance is given asXmin=n1λ1Ddhere,n1=5D = 2md = 2mm = 2×10−3mso,Xmin=[5×12000×10−10×2]2×10−3thus, we getXmin = 6mm hence B option is the correct answer

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