1Which of these has the same dimensions as magnification?
Magnification and strain both have the dimensions [M⁰ L⁰ T⁰].
OpticsClass 12, Ray Optics and Optical Instruments
Dimensional formula of Magnification
[M0 L0 T0]
Image size divided by object size, a pure number.
How to get the dimensional formula of magnification
- Start from the definition: magnification = length / length.
- Put in the dimension of each part: [L] / [L].
- 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
- Refractive index
Equal dimensions do not make them the same quantity. Compare magnification with the others in the full grid.
Three questions on magnification
2Which of these has no dimensions at all?
Magnification 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].
Magnification: quick answers
What is the dimensional formula of magnification?
The dimensional formula of magnification is [M⁰ L⁰ T⁰]. It comes from magnification = length / length.
What is the SI unit of magnification?
Magnification has no unit, because it is a pure number.
Is magnification dimensionless?
Yes. Magnification is a ratio of like quantities, so every power in its dimensional formula is zero: [M⁰ L⁰ T⁰].