1Which is the dimensional formula of illuminance?
Illuminance works out to [L⁻² cd].
OpticsClass 12, Ray Optics and Optical Instruments
Dimensional formula of Illuminance
[L-2 cd]
Luminous flux falling on unit area, one lumen per square metre.
How to get the dimensional formula of illuminance
- Start from the definition: illuminance = luminous flux / area.
- area = length × length, so area is [L] × [L] = [L2].
- solid angle = area / area, so solid angle is [L2] / [L2] = [M0 L0 T0].
- luminous flux = luminous intensity × solid angle, so luminous flux is [cd] × [M0 L0 T0] = [cd].
- Put in the dimension of each part: [cd] / [L2].
- Add the powers of each base quantity: [L-2 cd].
Three questions on illuminance
2What is the SI unit of illuminance?
The SI unit of illuminance is the lux (lx).
3Do illuminance and magnification have the same dimensions?
Illuminance is [L⁻² cd] but magnification is [M⁰ L⁰ T⁰].
Illuminance: quick answers
What is the dimensional formula of illuminance?
The dimensional formula of illuminance is [L⁻² cd]. It comes from illuminance = luminous flux / area.
What is the SI unit of illuminance?
The SI unit of illuminance is the lux (lx).
Is illuminance dimensionless?
No. Illuminance has the dimensions [L⁻² cd].