Answer to Question #157580 in Optics for What's ans?

Question

The diameter of 20th dark ring in a Newton's Ring system viewed normally is 0.6 c.m. Calculate the thickness of corresponding air film if wavelength of light used is 6X10 cm.

Answer 1

Let's write the condition for dark ring:

$$D_n=\sqrt{4n\lambda R}.$$

From this formula we can find $R$:

$$R=\dfrac{D_n^2}{4n\lambda}=\dfrac{(6.0\cdot10^{-3}\ m)^2}{4\cdot20\cdot6\cdot10^{-7}\ m}=0.75\ m.$$

Finally, we can find the thickness of corresponding air film:

$$t=\dfrac{r_n^2}{2R}=\dfrac{(3.0\cdot10^{-3}\ m)^2}{2\cdot 0.75\ m}=6\cdot10^{-6}\ m=6\ \mu m.$$

Answer:

$t=6\ \mu m.$