Question

Plot the graph showing variation of focal length of a plano convex lens in air with the change in refractive index(u) of material of the lens

Answer 1

The relationship between them relies on the radius of curvature of the interface. The formula that relates them is:

F = (n’-n)/r

Where F = power of lens in diopters, n’ = refractive index of the receiving media (usually lens when light enters, surrounding media [usually air] when light leaves the lens), n = refractive index of media of origin (usually surrounding media when light enters the lens, and lens index when light leaves the lens), and r = radius of curvature of the lens in metres.

A flat surface (r = infinity) will always give a power of 0, while as long as there is a difference in the index between the lens and the surrounding media, if theres a curvature (no matter how small), a lens power will come about.

F = (n’ - n) / inf => 0, for all (n’-n) >0 & <0.

The key feature of this is the difference between the surrounding media and lens, and the radii of curvature. For example a +8.00 lens* can be achieved with either:

1.49 (standard plastic), r = 6.125cm, 0.06125m

F = (n’-n)/r = (1.49–1)/0.06125 = +8.00

1.59 (polycarbonate), r = 7.375cm, 0.07375m

F = (n’-n)/r = (1.59–1)/0.07375 = +8.00

1.74 (thinnest conventional use plastic), r = 9.25cm, 0.0925m

F = (n’-n)/r = (1.74–1)/0.0925 = +8.00

Notice how all the focal lengths (1/8.00 = 12.5cm) remains constant, but the radii are changed. This leads to a flatter (and ultimately thinner) lens. If the radii was kept constant and the index changed, the power would alter to:

1.49 (standard plastic), r = 6.125cm, 0.06125m Reference

F = (n’-n)/r = (1.49–1)/0.06125 = +8.00

1.59 (polycarbonate), r = 6.125cm, 0.06125m

F = (n’-n)/r = (1.59–1)/0.06125 = +9.63

1.74 (thinnest conventional use plastic), 6.125cm, 0.06125m

F = (n’-n)/r = (1.74–1)/0.06125 = +12.08

These lenses would all have the same shape, thickness and would only differ by power.

So while an alteration of index can alter power proportionally, the relationship is better described by the inverse relationship with the radius of curvature.

Hope this helps