Newton's Rings Experiment
Determination of Wavelength of Sodium Light
1. Aim
To determine the wavelength of sodium light using Newton’s rings formed between a plano-convex lens and a plane glass plate.
2. Apparatus Used
Newton's Ring Apparatus
Complete setup with adjustable components
Complete setup with adjustable components
Plano-convex Lens
Large radius of curvature
Large radius of curvature
Plane Glass Plate
Optically flat surface
Optically flat surface
Sodium Vapor Lamp
Monochromatic light source (λ ≈ 589 nm)
Monochromatic light source (λ ≈ 589 nm)
Traveling Microscope
For measuring ring diameters
For measuring ring diameters
Glass Wedge
For fine adjustment
For fine adjustment
3. Diagram
Experimental Setup
Cross-sectional View
4. Theory
Newton's rings are circular interference fringes formed when a plano-convex lens is placed on a plane glass plate with its curved surface in contact with the plate. A thin air film of varying thickness is formed between the lens and the plate.
Key Concepts:
- Interference: Two coherent light rays interfere after reflection from the top and bottom surfaces of the air film
- Phase Change: Ray reflected from the denser medium (glass) undergoes a phase change of π
- Path Difference: Depends on the thickness of the air film at different points
When monochromatic light falls on this arrangement, interference occurs between:
- Light reflected from the bottom surface of the lens (no phase change)
- Light reflected from the top surface of the glass plate (phase change of π)
Due to the phase change of π at the glass-air interface, the effective path difference for constructive interference (bright rings) is:
Loading formula...
For destructive interference (dark rings):
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Where: t = thickness of air film, n = order of interference, λ = wavelength of light
5. Formula
For Dark Rings (Destructive Interference):
Loading formula...Diameter of nth Dark Ring:
Loading formula...Wavelength Formula:
Loading formula...
Where:
• rn = radius of nth dark ring
• Dn = diameter of nth dark ring
• R = radius of curvature of plano-convex lens
• λ = wavelength of sodium light
• n, m = ring numbers (n > m)
• rn = radius of nth dark ring
• Dn = diameter of nth dark ring
• R = radius of curvature of plano-convex lens
• λ = wavelength of sodium light
• n, m = ring numbers (n > m)
6. Procedure
1
Setup: Place the plano-convex lens on the plane glass plate with the curved surface touching the plate. Ensure good contact at the center.
2
Illumination: Switch on the sodium vapor lamp and allow it to warm up for proper monochromatic light emission.
3
Alignment: Adjust the glass plate (beam splitter) at 45° to direct light onto the lens-plate combination.
4
Observation: Look through the traveling microscope and adjust the focus to clearly see the Newton's rings pattern.
5
Measurement: Measure the diameters of at least 10 dark rings by noting the positions of opposite ends of each ring.
6
Recording: Record all measurements in the observation table and calculate the square of diameters.
7
Analysis: Plot a graph of D² vs ring number and determine the wavelength from the slope.
⚠️ Important: Handle the optical components carefully and ensure proper alignment for accurate measurements.
7. Observation Table
Radius of curvature of plano-convex lens, R = _______ cm
| Ring No. (n) | Left Side Reading | Right Side Reading | Diameter Dn (cm) | Dn² (cm²) | ||
|---|---|---|---|---|---|---|
| MSR | PSR | MSR | PSR | |||
| 5 | ||||||
| 6 | ||||||
| 7 | ||||||
| 8 | ||||||
| 9 | ||||||
| 10 | ||||||
| 11 | ||||||
| 12 | ||||||
| 13 | ||||||
| 14 | ||||||
| 15 | ||||||
Note: MSR = Main Scale Reading, PSR = Partial Scale Reading
Diameter = |Right Reading - Left Reading|
Diameter = |Right Reading - Left Reading|
8. Calculations
Method 1: Using Individual Rings
Loading formula...Method 2: Using Ring Difference (More Accurate)
Loading formula...Sample Calculation:
Let's say for rings n = 15 and m = 5:
- D₁₅² = _____ cm²
- D₅² = _____ cm²
- R = _____ cm
- n - m = 15 - 5 = 10
Loading formula...
Repeat this calculation for different ring pairs and find the average wavelength.
Expected Result: λ ≈ 589 nm (for sodium light)
9. Result
Wavelength of Sodium Light
λ = _______ nm
Percentage Error = _______%
Conclusion:
The wavelength of sodium light determined using Newton's rings method is _______ nm, which is in good agreement with the standard value of 589 nm for sodium D-line.
Error Analysis:
Compare your result with the accepted value and calculate percentage error:
% Error = |((Experimental - Theoretical)/Theoretical)| × 100%
Compare your result with the accepted value and calculate percentage error:
% Error = |((Experimental - Theoretical)/Theoretical)| × 100%
10. Precautions
⚠️ Essential Precautions
1
Optical Alignment: Ensure proper alignment of the optical system to get clear and concentric rings.
2
Lens Contact: The plano-convex lens should make proper contact with the glass plate at the center without any dust particles.
3
Clean Surfaces: Clean all optical surfaces with lint-free cloth to avoid scattered light and unclear rings.
4
Stable Setup: Ensure the experimental setup is stable and free from vibrations during measurements.
5
Measurement Accuracy: Take readings carefully and avoid parallax error while using the traveling microscope.
6
Ring Selection: Select well-defined dark rings for measurement, avoiding the central bright spot.
7
Multiple Readings: Take measurements for multiple ring pairs to minimize random errors.
8
Monochromatic Light: Allow the sodium lamp to warm up completely for stable monochromatic light.
11. Viva Voice Questions
🎓 Common Viva Questions & Answers
Q1
What are Newton's rings?
Answer: Newton's rings are circular interference fringes formed when a plano-convex lens is placed on a plane glass plate, creating an air film of varying thickness.
Answer: Newton's rings are circular interference fringes formed when a plano-convex lens is placed on a plane glass plate, creating an air film of varying thickness.
Q2
Why is monochromatic light used?
Answer: Monochromatic light is used to get clear and distinct interference fringes. White light would produce colored fringes that overlap and become indistinct.
Answer: Monochromatic light is used to get clear and distinct interference fringes. White light would produce colored fringes that overlap and become indistinct.
Q3
Why is the center of Newton's rings dark?
Answer: At the center, the air film thickness is nearly zero, but there's still a phase change of π at the glass-air interface, resulting in destructive interference and a dark center.
Answer: At the center, the air film thickness is nearly zero, but there's still a phase change of π at the glass-air interface, resulting in destructive interference and a dark center.
Q4
What happens if we use white light instead of sodium light?
Answer: With white light, we get colored rings because different wavelengths interfere at different positions, creating a spectrum of colors in each ring.
Answer: With white light, we get colored rings because different wavelengths interfere at different positions, creating a spectrum of colors in each ring.
Q5
Why do we measure diameters instead of radii?
Answer: Measuring diameters is more accurate as it eliminates errors in locating the exact center of the rings.
Answer: Measuring diameters is more accurate as it eliminates errors in locating the exact center of the rings.
Q6
What is the condition for dark rings?
Answer: For dark rings: 2t = (2n-1)λ/2, where t is the air film thickness, n is the order, and λ is the wavelength.
Answer: For dark rings: 2t = (2n-1)λ/2, where t is the air film thickness, n is the order, and λ is the wavelength.
Q7
Why don't we use the first few rings for measurement?
Answer: The first few rings are not perfectly circular and are difficult to measure accurately due to imperfect contact at the center.
Answer: The first few rings are not perfectly circular and are difficult to measure accurately due to imperfect contact at the center.
Q8
What is the principle behind Newton's rings?
Answer: It's based on the interference of light waves reflected from the top and bottom surfaces of a thin air film.
Answer: It's based on the interference of light waves reflected from the top and bottom surfaces of a thin air film.
Q9
How does the ring size change with wavelength?
Answer: Larger wavelengths produce larger rings since the ring diameter is proportional to the square root of wavelength.
Answer: Larger wavelengths produce larger rings since the ring diameter is proportional to the square root of wavelength.
Q10
What are the applications of Newton's rings?
Answer: Measuring wavelength of light, testing optical surfaces for flatness, determining refractive index, and quality control in optics.
Answer: Measuring wavelength of light, testing optical surfaces for flatness, determining refractive index, and quality control in optics.
Q11
Why is sodium light preferred for this experiment?
Answer: Sodium light is nearly monochromatic (589 nm), intense, and easily available, making it ideal for interference experiments.
Answer: Sodium light is nearly monochromatic (589 nm), intense, and easily available, making it ideal for interference experiments.
Q12
What happens if the lens is pressed harder on the glass plate?
Answer: The rings become smaller and move toward the center as the air film thickness decreases with increased pressure.
Answer: The rings become smaller and move toward the center as the air film thickness decreases with increased pressure.