This
method for determining the wavelength of light was proposed by Sir Isaac Newton in his book
Opticks, published in 1717. The experimental arrangement is shown in Figure 1.

A
plano-convex lens of large radius of curvature R is placed on a plane glass plate with its curved
surface downwards and is illuminated from above with a parallel beam of monochromatic light.
Some of the light is reflected from the upper surface of the glass plate and some from the lower
surface of the lens; interference thus occurs by division of amplitude, the fringes being localised
in the air gap between the lens and plate.

At any point a distance r from the axis of the
lens the path difference will be 2h, where h is the distance between the lens and the plate at
that point (See Figure 2). The interference fringes are circular because the system is
symmetrical about the centre of the lens. The radius of any ring is given by:

(2R - h)h =
r^{2} so r^{2} = 2Rh – h^{2}

But h^{2} is small compared with 2Rh
and so: 2Rh = r^{2}

The path difference (2h) is therefore r^{2}/R

A phase change of π occurs when the light reflects from the top surface of the plate but
not at the lower surface of the lens, and therefore:

For a dark ring viewed by reflection: mλ = r

where m = 0, 1, 2, 3, etc and r

If a graph is plotted of r

(r

where r

When doing the experiment it is much easier (and more accurate) to measure the diameter of the rings and then calculate their radius. A dark central spot should be obtained when viewed by reflection.

The
rings can be viewed by transmission by putting the microscope below the plate, and if this is
done the equations for bright and dark rings should be interchanged as two phase changes will
occur, producing an effective phase difference of 2π. A bright central spot should be
obtained.

If white light is used a few coloured rings will be seen due to the different
wavelengths of the different colours of light.

This effect may be used to measure the refractive index of the liquid; the method is a good one since it is accurate and easy to perform, and only a small amount of the liquid is needed.

Calculate the ratio of the diameters of the fifth interference rings with and without water (refractive index 1.33) between the lens and the plate if the radius of curvature of lens is 0.50 m.

Without water:

r

With water:

r

Therefore:

ratio of radii = 1/(1.33)

A series of rings formed in Newton's rings experiment with sodium light was viewed by reflection. The diameter of the m

For the m

and for the (m + 10)

where R is the radius of curvature of the lens surface.

Therefore:

0.34

Therefore, substituting for m, R = 1.66 metres.