Question

White coherent light `(400 nm-700 nm)` is sent through the slits of a YDSE. `D=0.5 mm`, D=50 cm. There is a hole in the screen at a point `1.0 mm` away (along the width of the fringes) from the central line.
(a) Which wavelength will be absent in the light coming from the hole?
(b) Which wavelength(s) will have a strong intensity?

Answer 1

`d=0.5 mm, D=50 cm, y=1 mm`
(a) For absent wavelength, use condition of minima
`y=(2n+1)(Dlambda)/(2d)`
`10^(-3)=((2n+1)(0.5)lambda)/(2xx0.5xx10^(-3))`
`lambda=(2xx10^(-6))/((2n+1))m=2000/(2n+1)xx10^(-9) m`
`=2000/(2n+1)nm`
`n=0, lambda=2000 nm`
`n=1, lambda=2000/3=667 nm`
`n=2, lambda=2000/5=400 nm`
In the range `(400-700 nm)`, absent wavelengths are `400 nm, 667 nm`
(b) For wavelengths of strong intensity, use condition of maxima
`y=n(Dlambda)/d`
`10^(-3)=(n(0.5)(lambda))/(0.5xx10^(-3))
lambda=10^(-6)/n=1000/nxx10^(-9) m=1000/n nm`
`n=1, lambda=1000 nm`
`n=2, lambda=500 nm`
`n=3, lambda=393 nm`
In the range `(400-700 nm)`, wavelength having strong intensity`=500 nm`