when white light travels through glass the refrective index n is found to vary with wavelength lambda as n=A+(B/lambda^2), where A and B are constants. determine the dimensions of A and B.

we have the following relation

n = A + B/λ^{2}

now as we have two terms being added to each other their dimensions should be equal to each other and thus to the terms on the left.

so,

Dimensions of n = Dimensions of a = Dimensions of B/λ^{2}

now, as the refractive index n is dimensionless, **A is also dimensionless**, thus

n = A = 1 = B/λ^{2}

the dimensions of B will be that of A.λ^{2} = λ^{2}

as λ^{2} has a dimensions of m^{2}, **B will also have dimensions of m**^{2}.

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