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/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.