Newton's Rings Experiment

Aim

Determination of the wavelength of Sodium light by Newton’s rings method.

Apparatus

• Sodium lamp (monochromatic light source)
• Plano-convex lens (with a large radius of curvature)
• Optically flat glass plate
• Traveling microscope
• Glass plate
• Magnifying lens

Pre-Lab Questions

1. What is meant by interference of light? How does it occur in Newton's rings?
   Interference of light is the phenomenon where two or more light waves superpose to produce a resultant wave of greater or lesser amplitude. In Newton's rings, interference occurs between light waves reflected from the top surface of the air film (between the lens and glass plate) and the bottom surface. The phase difference due to the path length variation in the air film leads to constructive (bright rings) and destructive (dark rings) interference.
2. State the principle of superposition of waves
   The principle of superposition of waves states that when two or more waves overlap in space, the resultant displacement at any point is the algebraic sum of the displacements of the individual waves at that point
3. Why is a sodium lamp used as the light source in this experiment?
   A sodium lamp is used because it emits monochromatic light (primarily at 589 nm), which produces a clear and distinct interference pattern. Polychromatic light (e.g., white light) would cause overlapping patterns of different wavelengths, making the rings indistinct and harder to measure.
4. What is the significance of using a plano-convex lens with a large radius of curvature?
   A large radius of curvature ensures that the air film between the lens and glass plate changes thickness gradually, producing well-spaced and observable rings. A smaller radius would result in closely spaced rings, making measurements difficult.
5. What are some necessary conditions for sustained interference?
   For sustained interference, waves must come from coherent sources with the same frequency, and comparable amplitudes, while maintaining a small path difference to ensure a stable interference pattern.
6. How does the air film between the lens and glass plate contribute to the formation of rings?
   The air film’s thickness varies radially from the point of contact, causing a path difference between the reflected waves. This path difference, combined with a phase change upon reflection, leads to interference, forming alternate bright and dark concentric rings.
7. What is the difference between bright and dark fringes in Newton's rings?
   Bright fringes occur due to constructive interference when the path difference is an integral multiple of the wavelength (\(2t = m\lambda\)). Dark fringes occur due to destructive interference when the path difference is an odd multiple of half the wavelength (\(2t = (2m+1)\lambda/2\)), with an additional phase shift of \(\pi\) from reflection at the denser medium.
8. What is a coherent source of light?
   A coherent source of light emits waves that have a constant phase difference and the same frequency.

Theory

Newton's rings are formed due to the interference of light waves reflected from the top and bottom surfaces of a thin air film enclosed between a plano-convex lens and a flat glass plate. When monochromatic light (e.g., sodium light) is incident on the setup, the interference between the reflected waves produces a pattern of alternate bright and dark concentric rings. The thickness of the air film increases radially outward from the point of contact, causing a phase difference that results in constructive and destructive interference. The wavelength of the light can be determined by measuring the diameters of these rings and using the relationship between the ring diameter, the radius of curvature of the lens, and the wavelength of light.

Working Formula

The diameter of the \(n^{th}\) dark ring is given by:
\[ \lambda = \frac{D^2_{n+p}-D_n^2}{4pR} \]
Where:
- \(D_{n+p}\) = Diameter of the \( (n+p)^{th}\) dark ring
-\(D_{n}\) = Diameter of the \( n^{th}\) dark ring
- \( p \) is an inter number \( (p = (n+p)-n) \)
- \(R\) = Radius of curvature of the plano-convex lens
- \(n\) = Order of the ring (2, 4, 6, ...)

Least Count

\[ L C = \frac{\text{One Main scale division}}{\text{Number of Vernier Scale divisions}} \] \[L C = \frac{1}{100} = 0.01 \text{mm} \]

Diagram

Procedure

1. Set up the apparatus by placing the plano-convex lens on the flat glass plate, ensuring clean surfaces.
2. Position the sodium lamp and the 45° inclined glass plate to direct light onto the lens-glass interface.
3. Adjust the traveling microscope above the setup until the Newton's rings pattern is clearly visible.
4. Focus the microscope on the center of the ring pattern and note the position of the crosshairs.
5. Measure the diameter of 2, 4, 6, 8, 10 & 12 dark rings by moving the microscope horizontally and recording the readings on both sides of the center.
6. Record all observations in the observation table.
7. Repeat the measurements to ensure accuracy.

Observation Table

Sl. No.	Ring Number	Reading on Microscope		Diameter of Ring (D) = R₁ - R₂	D²
		Left R₁ = M.S.R + (V.C × L.C.)	Right R₂ = M.S.R + (V.C × L.C.)
1	12
2	10
3	8
4	6
5	4
6	2

Radius of curvature of the lens (\(R\)) = 850 mm.

Model Graph

Calculations

1. Using the formula \[ \lambda = \frac{D_{n+p}^2 - D_n^2}{4pR} \]
2. Compute \(\lambda\) and take the average of multiple readings for accuracy.

Example:

\[ \lambda = \frac{(24 - 20)\times (10^{-3})^2}{4\times2\times 850\times 10^{-3}} \] \[ \lambda = \frac{4 \times 10^{-3}}{4\times 2 \times 850} m \] \[ \lambda = \frac{4 \times 10^{-3}}{6800} m \] \[ \lambda = 5.882 \times 10^{-4} \times 10^{-3} m \] \[ \lambda = 588.2 \times 10^{-9} m \Rightarrow 588.2 nm \]
\[ Error (\%) = \left | \frac{\lambda_{calculated} - \lambda_{standarad}}{ \lambda_{standard} } \right | \]

\[ \lambda_{standarad} = 589 nm \]

Precautions

1. Ensure the glass plate and lens surfaces are clean and free from dust or scratches.
2. Use a monochromatic light source (sodium lamp) to avoid overlapping of multiple wavelengths.
3. Align the traveling microscope carefully to measure diameters accurately.
4. Perform the experiment in a dark room to enhance the visibility of the rings.

Applications

1. Determination of the wavelength of light sources in optical experiments.
2. Measurement of the radius of curvature of lenses in lens manufacturing.
3. Study of thin film interference in optics and material science.
4. Used in quality control for checking the flatness of surfaces.

Post-Lab Questions

1. Why do the rings get closer together as the ring order (\(n\)) increases?
   The diameter of the \(n^{th}\) ring is proportional to \(\sqrt{n}\) (from \(D_n^2 = 4n\lambda R\)). As \(n\) increases, the increase in \(D_n\) becomes smaller relative to the previous ring, causing the rings to appear closer together.
2. What would happen if a white light source were used instead of a sodium lamp?
   A white light source contains multiple wavelengths, producing overlapping interference patterns for each wavelength. This results in colored rings near the center (due to varying constructive interference conditions) and a less distinct pattern farther out, making precise measurements difficult.
3. How does the radius of curvature (\(R\)) affect the size of the rings?
   The diameter of the rings is proportional to \(\sqrt{R}\) (from \(D_n^2 = 4n\lambda R\)). A larger \(R\) increases the diameter of the rings, making them more spread out and easier to measure, while a smaller \(R\) reduces the ring size and spacing.
4. Explain why the center of Newton's rings is dark in reflected light.
   At the center, the air film thickness is zero, and the path difference is zero. However, light reflected from the glass plate (denser medium) undergoes a \(\pi\) phase shift, while the reflection from the lens does not. This results in destructive interference, producing a dark spot at the center.
5. How can this method be modified to measure the refractive index of a liquid?
   Introduce a liquid (e.g., water or oil) between the lens and glass plate. The wavelength of light in the liquid becomes \(\lambda/n\), where \(n\) is the refractive index of the liquid. Measure the ring diameters with and without the liquid, and use the modified formula \(D_n^2 = 4n(\lambda/n)R\) to calculate \(n\) by comparing the two sets of results.
6. Why Newton’s rings are circular?
   The air gap between the two surfaces varies in thickness in a circularly symmetric manner, creating concentric bright and dark rings where constructive and destructive interference occur, respectively. The circular symmetry of the lens causes the rings to be circular.

Outcomes

• The wavelength of sodium light was successfully determined using Newton's rings and found to be approximately 589 nm (average value for sodium D-lines).
• The experiment demonstrated the principles of interference and the dependence of ring diameter on wavelength and lens curvature.
• Accurate measurement techniques and careful observation improved the precision of the results.

Visual Explantion of Newton's Rings Experiment