Q16Engineering Physics

The Newton's rings experiment provides a highly precise interferometric method for determining the wavelength of an unknown monochromatic light source by analyzing the geometry of the resulting circular interference fringes.

1. Theoretical Formula

For a Newton's rings setup viewed in reflected light, the condition for destructive interference (producing dark rings) dictates that the square of the diameter of the $n$-th dark ring is directly proportional to the wavelength ($\lambda$), the order of the ring ($n$), and the radius of curvature ($R$) of the plano-convex lens.

By algebraically rearranging this fundamental equation, we can isolate the unknown wavelength $\lambda$:

2. Extraction and Conversion of Given Data

To prevent catastrophic order-of-magnitude calculation errors, every given value must be meticulously converted into standard SI units (meters) before substitution.

• Order of the dark ring ($n$) = $10$
• Diameter of the 10th dark ring ($D_{10}$) = $0.5\text{ cm}=0.5\times 10^{-2}\text{ m}$
• Radius of curvature of the lens ($R$) = $100\text{ cm}=1.0\text{ m}$

3. Step-by-Step Substitution and Calculation

Substitute these standard values into the rearranged formula:

First, carefully square the diameter term in the numerator:

Evaluate the denominator:

Now, perform the final division:

Adjust the scientific notation to standard form:

4. Final Conversion to Angstroms

In optics, it is standard practice to express wavelengths in Angstroms ($\text{A˚}$), where $1\text{ A˚}=10^{-10}\text{ m}$. We multiply our result in meters by $10^{10}$:

This specific wavelength ($6250\text{ A˚}$) lies in the red-orange region of the visible light spectrum.