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Asked in GSEB Board August 2020 · Dimensional formula of a named quantity
Given: the power of a lens.
Idea: the power of a lens is the reciprocal of its focal length, P=1/f, with f measured in metre.
[f]=L¹, so [P]=L⁻¹, which written out in full is M⁰L⁻¹T⁰.
One dioptre is one reciprocal metre, which is why a converging lens of focal length 50 cm is a +2 D lens.
So the dimensional formula for the power of a lens is M⁰L⁻¹T⁰ -- not the M¹L²T⁻³ of mechanical power.
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