2 I design an ideal plano-convex lens, cut from a hyperboloid. I set things up s

Question

2

I design an ideal plano-convex lens, cut from a hyperboloid. I set things up so that the focal point is on the left, as is the curved side, and the distance from the focal point to the flat side is called f. The thickness at the center is fixed at some value x. Suppose that I make it thicker, i.e. I cut a larger piece from the exact same hyperboloid. Does the distance from the focal point to the flat side change? Why or why not? In the scenario in the previous part, does the distance from the focal point to the center of the curved side change? Why or why not?

Explanation / Answer

(1) We know that focal length of the equation
1/f = (n-1)(1/R1 - 1/R2 + (n-1)d / nR1R2)
where d is thickness , R1 and R2 is the radii of curvature of the curved and plane surface
therefore R2 will be infinite.
Hence focal length is independent of the thickness.
(2) If focal length remain unchanged then distance will also remain same.

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