Newton's Rings and plano-convez lens

[simplicity12]

Homework Statement

A plano-convez lens (flat on one side, convez on the other) rests with its curved side on a flat glass surface. The lens is illuminated from above by light of wavelength 521 nm. A dark spot is observed at the centre, surrounded by 15 concentric dark rings (with bright rings in between). How much thicker is the air wedge at the position of the 16th dark ring than at the centre?

Homework Equations

There were no equations introduced in this section.

The Attempt at a Solution

The answer says 3.90 X 10^-7m. By multiplying the wavelength by 15 and then dividing it by 2, i get this answer.. by why? Is there actually an equation for these type of problems?

 

[Mentz114]

It's interference, and there is a formula. Have a look at this -
http://en.wikipedia.org/wiki/Newton's_rings

 

[m2003]

I would like to clarify that the answer given (3.90 x 10^-7m) is incorrect. The correct equation to use in this situation is the equation for the thickness of an air wedge, which is t = nλ/2, where t is the thickness, n is the refractive index of the medium (in this case, air), and λ is the wavelength of light.

In this problem, we are given the wavelength (521 nm) and the number of dark rings (15), so we can rearrange the equation to solve for the thickness at the 16th dark ring:

t = (nλ/2) * (15+1) = (1 * 521 nm / 2) * 16 = 4168 nm = 4.168 μm

Therefore, the thickness at the 16th dark ring is 4.168 μm, which is much larger than the incorrect answer of 3.90 x 10^-7m. This shows the importance of using the correct equations and understanding the principles behind them in scientific problem-solving.