The lens-maker's formula
The refractive index of the material of the lens a
can be introduced into the formula.
The radius of curvature R = h/
q for small
q, but n = sin
f/sin
q and therefore n =
f/
q for small angles.
So
f = n
q for small values of
q, that is for rays
close to the principal axis of the lens.
But d =
f -
q. Therefore: (n – 1)
q = h/f and
q = h/R and so (n – 1)/R = 1/f = 1/u + 1/v
Therefore
for a lens we have:
where R and S are the radii of
curvature of the two faces of the lens. This formula is known as the lens-maker's formula.
