Question

How do you derive the lens maker's equation? ...?

Answer 1

Using Snell’s law ( n1 sin θi = n2 sin θr ) at point A gives

1)        sin i1 = n sin r1             

2)        i1 = n r1

3)        i1 = α1 + β1

4)        r1 = β1 - γ

5)        α1 + β1 = n(β1 - γ)

6)        sin i2 = n sin r2

7)        i2 = n r2

8)        i2 = α2 + β2

9)        r2 = β2 + γ

10)      α2 + β2 = n(β2 + γ)

11)      α1 + α2 = (n - 1)(β1 + β2)

12)  1/s + 1/s' = (n - 1)(1/R1 + 1/R2)

13) 1/f = (n - 1)(1/R1 - 1/R2)

14) 1/s + 1/s' = 1/f