The relation for refraction of light rays (travelling from medium 1 to medium 2) at a single spherical surface (concave or convex) :
μ₂ / v - μ₁ / u = (μ₂ - μ₁) / R
μ₁, μ₂ are the refractive indices of the media 1 and 2 respectively.
When there are two surfaces,
μ₂ / v₁ - μ₁ / u = (μ₂ - μ₁) / R₁
μ₁ / v - μ₂ / v₁ = (μ₁ - μ₂) / R₂ , as v₁ is the object distance for the 2nd surface
μ₁ (1/v - 1/u) = (μ₂ - μ₁) * [1/ R₁ - 1 / R₂)
1/v - 1/u = (μ₂/μ₁ - 1) * [1/ R₁ - 1 / R₂)
for a thin bi-convex lens, R₂ = - R₁ = R
1/v - 1/u = (μ₂ /μ₁ - 1) * 2 / R = (μ₂₁ -1) 2 / R
μ₂₁ = μ is the refractive index of the medium of lens wrt to the medium in which the lens is kept.
As, 1/ v - 1/ u = 1/f is the thin lens formula.
Thus the lens makers formula is :
1/f = (μ -1) * 2 / R
f = focal length of the bi convex lens..
R = f
Then substituting this in the lens makers formula above, we get
μ = 1.5