Newton’s rings - Measurement of wavelength and refractive index

Athul Kurian
Newton's Rings

Newton's Rings - Measurement of Wavelength and Refractive Index

Newton's Rings Setup:

  1. Apparatus:
    • A plano-convex lens (a lens with one flat surface and one curved surface).
    • A flat glass plate.
    • Monochromatic light source (light of a single wavelength, such as from a sodium lamp).
    • A microscope.
  2. Setup:
    • Place the plano-convex lens on the flat glass plate. Ensure good optical contact between the lens and the plate.
    • Illuminate the setup with monochromatic light. Adjust the angle and position of the light source for optimal results.
    • Observe the interference pattern formed between the lens and the plate. Newton's rings will be visible as concentric circles.

Measurement of Wavelength:

  1. Counting Rings:
    • Use a microscope to observe the pattern of rings. Count the number of rings from the center outward.
    • The ring pattern is formed due to constructive and destructive interference of light waves reflected between the lens and the glass plate.
  2. Wavelength Calculation:
    • The diameter of each ring (\(D\)) can be measured using the microscope.
    • The radius of each ring (\(r\)) is then calculated as \( r = \frac{D}{2} \).
    • The wavelength (\(\lambda\)) of the light is related to the radius of the rings by the formula: \( \lambda = \frac{2 \cdot n \cdot r}{m} \), where \( n \) is the refractive index of the medium, and \( m \) is the order of the ring.

Measurement of Refractive Index:

  1. Relationship:
    • The radius of the \(n\)th ring is related to the refractive index (\(n\)) of the medium by the equation: \( r = \sqrt{n \cdot R \cdot \lambda} \), where \( R \) is the radius of curvature of the lens.
  2. Experiment:
    • Measure the radius of several rings for different orders (\(m\)) using the microscope.
    • Plot a graph of \(r^2\) against \(m\).
    • The slope of the graph is related to \(n \cdot R \cdot \lambda\).
    • By knowing the wavelength (\(\lambda\)), the refractive index (\(n\)) can be determined.

Tips:

  • Use monochromatic light to ensure a clear interference pattern.
  • Ensure good optical contact between the lens and the glass plate for accurate results.
  • Precise measurements of ring diameters and orders are crucial for accurate calculations.

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