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A ray of light is incident on a glass slab at grazing incidence. The refractive indexof the material of the slab is given by mu=sqrt((1+y) . If the thickness of the slab is d=2m, determing the equation of the trajectory of the ray inside the slab and the coordinates of the point where the ray exits from theslab. Take the origin to be at the point of entry of the ray. |
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Answer» Solution :We have `(dy)/(dx)=cot(theta_(y))=sqrt(mu_(y)^(2)-sin^(2)theta)/(SINTHETA)` Here, `mu=sqrt((1+y))` and `theta=90^(@)` Therefore, `(dy)/(dt)=y^(1//2)` Integratin with the boundary condition that `y=0` at `zx=0`, we GET `y=x^(2)//4`to be the equation of the PATH of the ray through the SLAB, the ray will obviously EXIT at thepoint `(2sqrt2m,2m)`. |
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