Question

In a Newton’s rings experiment (using light of free space wavelength 580nm), there is an air gap of height d between the glass plate and a plano-convex lens (see figure). The central fringe is observed to be bright.

The least possible value of d (in nm) is:

• A. 290
• B. 145
• C. 580
• D. 72.5

Answer 1

The Correct Option is A

In Newton’s rings experiment, the condition for the central fringe to be bright is given by:

\[ 2d = m\lambda \]

where:

• \( d \): Thickness of the air gap
• \( m \): Fringe order
• \( \lambda \): Wavelength of the light

Step 1: Condition for Least Possible Value of \( d \)

For the least possible value of \( d \), we take \( m = 1 \) (first order fringe) and \( \lambda = 580 \, \text{nm} \).

Step 2: Solve for \( d \)

From the condition \( 2d = \lambda \):

\[ d = \frac{\lambda}{2} = \frac{580}{2} = 290 \, \text{nm} \]

Conclusion:

The least possible value of \( d \) is:

\[ \boxed{290 \, \text{nm}} \]