i) Time taken by the ray to travel from S to P1 is = t1 = √u2 + b2/c
Time taken by the ray to travel from P1 to O is = t2 = v/c (1+ ½ b2/v2)
Time taken to travel through the lens is = tl = (n – 1)w(b)/c
Total time is = t = 1/c (u + v + ½ b2/D + (n – 1)(wo + b2/a))
D is the focal length as 1/D = 1/u + 1/v
ii) Differentiating the expression for time, we get
β = b/v = √(n-1)k1u/(u + v)v