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Two identical monochromaticlight sources...

Two identical monochromaticlight sources A & B intensity `10^(-15)W//m^(2)` produce wavelength of light `4000sqrt(3)Å` A glass of thickness 3mm is placed in the path of the ray as shown in figure the glass has a varible refractive index `n=1+sqrt(x)` where x (in mm) is distance of plate from left to right calculate total intensity at focal points F of the lens.

Text Solution

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The correct Answer is:
`4xx10^(-15)W//m^(2)`
`I=10^(-15)W//m^(2),lamda=4000sqrt(3)Å,t=3mm`
The path difference due to glass plate 3mm. ltbr. Path difference `=intds=int_(0)^(3mm)(n-1)dx`
`int_(0)^(3)(1+sqrt(x)-1)dx=(2)/(3)x^(3//2)=2sqrt(3)mm`
`therefore` Phase difference
`=(2pi)/(4000sqrt(3)xx10^(-10))xx2sqrt(3)xx10^(-3)=pixx10^(7-3)`
`therefore2pin=10^(4)xxpi`
At point I there is point of maxima `n=5xx10^(3)`
`therefore` intensity `=I+I+2sqrt(I)xxsqrt(I)cos10^(4)pi`
`=4I=4xx10^(-15)W//m^(2)`
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