Question

Establish the formula (μ₂/v - μ₁/u) = (μ₂ - μ₁/r)

Answer 1

Let A be an object and rays AM and AP be refracted to meet in A' (A' is the image of A)

Point N is very close to P, as the rays are paraxial using the geometry of the figure,

Using snell's law

As the rays are paraxial i and r are very small

Hence, μ₁ i =  μ₂ r..........(iii)

From (i) and (ii) we put the values of i and r in equation (ii)

 μ₁ (α + r) =  μ₂ (Y - β)

From figure