When the white light travels through the glass the refractive index of Glass is found to vary with wavelength as Meu= A + B/ lambda square .Using the principle of homeogenity of dimensions find the SI units in which the constants A and B must be expressed

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Solution

we have the following relation

n = A + B/λ²

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/λ²

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

n = A = 1 = B/λ²

the dimensions of B will be that of A.λ² = λ²

as λ² has a dimensions of m², B will also have dimensions of m².

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