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When light of wavelength lambda travels ...

When light of wavelength `lambda` travels through glass, the refractive index of glass varies with wavelength as `mu=A+(B)/(lambda^(2))`. What are the dimensional formulae of A and B?

A

`[M^(0)L^(0)T^(0)][M^(0)L^(2)T^(-1)]`

B

`[M^(0)L^(1)T^(-1)][M^(0)L^(2)T^(0)]`

C

`[M^(0)L^(0)T^(0)][M^(0)L^(2)T^(0)]`

D

`[M^(1)L^(0)T^(1)][M^(0)L^(1)T^(1)]`

Text Solution

Verified by Experts

The correct Answer is:
c
`mu=("Velocity of light in air")/("Velocity of light in glass")`
Thus `mu` is a dimensionless quantity
or `[mu]=[M^(0)L^(0)T^(0)]`.
`therefore` As all terms should have the same dimensions
`therefore` For `A, [A]=[mu]=[M^(0)L^(0)T^(0)]`
and `[(B)/(lambda^(2))]=[mu]`
`therefore [B]=[mu][lambda^(2)]=[M^(0)L^(0)T^(0)xxL^(2)]=[M^(0)L^(2)T^(0)]`
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