A)

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

Adding them,

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..

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b)

R = f

Then substituting this in the lens makers formula above, we get

μ = 1.5