Deriving back focal length using Fermat's principle

[Woolyabyss]

Homework Statement

The plano-convex lens has a diameter of 200 mm and the central thickness of 20 mm. The edge thickness is zero and the refractive index of glass is 1.5. Find the following parameters of the lens: (i) the back focal length

Homework Equations

N/A

The Attempt at a Solution

I've attached my attempt below. I'm assuming the time taken for light to travel from the tip to the focal length is equal to the time taken to travel to the center to the focal length.

 

[haruspex]

Looks right.