1Which of these has the same dimensions as refractive index?
Refractive index and ratio of specific heats both have the dimensions [M⁰ L⁰ T⁰].
OpticsClass 12, Ray Optics and Optical Instruments
Dimensional formula of Refractive index
[M0 L0 T0]
Speed of light in vacuum divided by the speed in the medium, a pure number.
How to get the dimensional formula of refractive index
- Start from the definition: refractive index = speed of light / velocity.
- speed of light = length / time, so speed of light is [L] / [T] = [L T-1].
- velocity = length / time, so velocity is [L] / [T] = [L T-1].
- Put in the dimension of each part: [L T-1] / [L T-1].
- Add the powers of each base quantity: [M0 L0 T0].
Quantities with the dimensions [M⁰ L⁰ T⁰]
- Angle
- Solid angle
- Coefficient of friction
- Coefficient of restitution
- Relative density
- Strain
- Poisson's ratio
- Reynolds number
- Emissivity
- Ratio of specific heats
- Sound level
- Relative permittivity
- Magnetic susceptibility
- Relative permeability
- Power factor
- Quality factor
- Magnification
Equal dimensions do not make them the same quantity. Compare refractive index with the others in the full grid.
Three questions on refractive index
2Which of these has no dimensions at all?
Refractive index is a ratio, so every power in its dimensional formula is zero.
3Which one has different dimensions from the others?
Focal length is [L]. The other three are all [M⁰ L⁰ T⁰].
Refractive index: quick answers
What is the dimensional formula of refractive index?
The dimensional formula of refractive index is [M⁰ L⁰ T⁰]. It comes from refractive index = speed of light / velocity.
What is the SI unit of refractive index?
Refractive index has no unit, because it is a pure number.
Is refractive index dimensionless?
Yes. Refractive index is a ratio of like quantities, so every power in its dimensional formula is zero: [M⁰ L⁰ T⁰].