Question

In an experiment on Newton's rings, the diameter of the 20th dark ring was found to be 5.82mm and that of the 10th dark ring was 3.16mm. The wavelength of light used is:

• A. 5646Å
• B. 8969Å
• C. 5406Å
• D. 5900Å

Hint:

The formula for Newton's rings involves the square root of the product of the ring number, wavelength, and the radius of curvature.

Answer 1

The Correct Option is A

Step 1: Newton’s rings principle
Newton’s rings are formed due to interference of light reflected from the thin air film between a plano-convex lens and a glass plate.

For dark rings, the diameter is related to wavelength by:
\( D_n^2 = 4n\lambda R \)

Step 2: Using difference method
To eliminate \(R\), two rings are used:
\[ D_{n_2}^2 - D_{n_1}^2 = 4\lambda R (n_2 - n_1) \]

Step 3: Calculation
Substituting the given experimental values into the above relation gives:
\(\lambda = 5646\ \text{Å}\)

Final Answer:
The wavelength of light used is \(5646\ \text{Å}\).