An interference experiment is a physics experiment that observes how amplitudes reinforce or cancel each other when two or more waves overlap.
Young’s double-slit experiment is a representative method for investigating light interference. When monochromatic light passes through two narrow slits, the light spreading from each slit overlaps and produces a pattern of bright and dark fringes on a screen.
Bright fringes occur where the two light waves overlap in phase and reinforce each other, while dark fringes occur where they overlap out of phase and cancel each other. By measuring the fringe spacing, slit separation, and distance to the screen, the wavelength of light can be determined.
This article assumes an interference experiment using laser light and a double slit, and summarizes the introduction, precautions, items to record, sample experimental values, calculations, sources of error, example results, and discussion examples.
Note:
This article is a study reference for discussing results obtained in physics experiments at universities and similar institutions. The experimental values shown are examples for explanation and are not actual measurement results.
Never look directly into a laser beam or point it toward anyone’s eyes or reflective objects. Be careful with specularly reflecting metals, glass, watches, accessories, and similar objects, and always follow the laboratory manual and the instructions of your instructor or teaching assistant when operating the apparatus.
What Is Light Interference?
When two waves reach the same location, their individual displacements are superposed. When crest overlaps crest or trough overlaps trough, the amplitude increases; when a crest overlaps a trough, the amplitude decreases.
For light, locations where the waves reinforce each other appear bright, while locations where they cancel appear dark. This repeating pattern of bright and dark regions is called interference fringes.
Conditions for Bright and Dark Fringes
Let the optical path difference from the two slits to an observation point be δ, and let the wavelength of light be λ. The condition for a bright fringe is:
δ = mλ
m is an integer: 0, ±1, ±2, ….
The condition for a dark fringe is:
δ = (m + 1/2)λ
Interference Fringes from a Double Slit
Let the slit separation be d, the distance from the slits to the screen be L, and the distance from the central fringe to the m-th bright fringe be xm.
When the screen distance is sufficiently large compared with the slit separation and fringe position, and the angle is small, the position of a bright fringe is approximately:
xm = mλL / d
If the spacing between adjacent bright fringes is Δx, then:
Δx = λL / d
Therefore, the wavelength of light is:
λ = dΔx / L
Main Items to Record in the Results
- Type of light source and nominal wavelength
- Double-slit separation
- Width of each slit
- Distance from the slits to the screen
- Position of the central bright fringe
- Positions of bright or dark fringes of each order
- Measured distance corresponding to multiple interference fringes
- Fringe spacing
- Calculated wavelength of light
- Average wavelength from repeated measurements
- Relative error from the nominal wavelength
- Brightness and sharpness of the interference fringes
- Symmetry of fringe positions on the left and right
- Angle of the optical axis relative to the screen
- Presence of ambient light or vibration
Instead of measuring only the distance between two adjacent fringes, measuring the distance from the center to a fringe several orders away, or measuring the distance spanning 10 fringes and dividing by the number of intervals, reduces reading error.
Sample Experimental Conditions
| Item | Sample Condition |
|---|---|
| Light source | Red semiconductor laser |
| Nominal wavelength | 650 nm |
| Slit separation d | 0.250 mm |
| Slit width | 0.050 mm |
| Screen distance L | 1.50 m |
| Measurement method | Measure positions from the central bright fringe to the fifth order on both sides |
| Smallest distance division | 1 mm |
| Number of measurements | 3 |
Sample Experimental Values
Positions of Bright Fringes of Each Order
| Bright-fringe order m | Left position (mm) | Right position (mm) | Distance between left and right (mm) | Average distance from center (mm) |
|---|---|---|---|---|
| 1 | −3.8 | 3.9 | 7.7 | 3.85 |
| 2 | −7.7 | 7.8 | 15.5 | 7.75 |
| 3 | −11.6 | 11.7 | 23.3 | 11.65 |
| 4 | −15.5 | 15.6 | 31.1 | 15.55 |
| 5 | −19.4 | 19.5 | 38.9 | 19.45 |
The distance from the center to each bright fringe is approximately proportional to its order. Therefore, the bright fringes are arranged at nearly equal intervals.
Example Fringe-Spacing Measurements
| Measurement | Distance spanning 10 fringes (mm) | Fringe spacing Δx (mm) | Wavelength λ (nm) |
|---|---|---|---|
| 1 | 39.0 | 3.90 | 650 |
| 2 | 38.8 | 3.88 | 647 |
| 3 | 39.2 | 3.92 | 653 |
When the Screen Distance Is Changed
| Screen distance L (m) | Fringe spacing Δx (mm) | Calculated wavelength (nm) |
|---|---|---|
| 1.00 | 2.60 | 650 |
| 1.25 | 3.25 | 650 |
| 1.50 | 3.90 | 650 |
| 1.75 | 4.54 | 649 |
The fringe spacing increases as the screen distance increases.
Calculation Method
Finding Fringe Spacing from Multiple Fringes
If the distance spanning 10 fringes is 39.0 mm:
Δx = 39.0 mm / 10
= 3.90 mm
Wavelength of Light
For a slit separation of 0.250 mm, fringe spacing of 3.90 mm, and screen distance of 1.50 m, first convert all units to meters.
d = 0.250 mm = 2.50 × 10−4 m
Δx = 3.90 mm = 3.90 × 10−3 m
λ = dΔx / L
= (2.50 × 10−4) × (3.90 × 10−3) / 1.50
= 6.50 × 10−7 m
= 650 nm
Finding the Wavelength from the Fifth Bright Fringe
If the distance from the center to the fifth bright fringe is 19.45 mm:
λ = dxm / mL
= (2.50 × 10−4) × (19.45 × 10−3) / (5 × 1.50)
= 6.48 × 10−7 m
= 648 nm
Average Wavelength
Average wavelength = (650 + 647 + 653) / 3
= 650 nm
Relative Error
For a nominal wavelength of 650 nm and an experimental value of 648 nm:
Relative error (%) = |experimental value − nominal value| / nominal value × 100
= |648 − 650| / 650 × 100
= approximately 0.31%
Finding the Wavelength from a Graph
If the bright-fringe position xm is plotted on the vertical axis and the order m on the horizontal axis, the slope a is:
a = λL / d
Therefore, the wavelength is:
λ = ad / L
Fitting a straight line to multiple fringe positions reduces the effect of individual reading errors.
Main Sources of Error
| Source of error | Effect on measurement | Likely tendency in results | Improvement |
|---|---|---|---|
| Error in reading fringe centers | It is difficult to determine the exact center of a bright fringe | Fringe spacing and wavelength vary | Measure across multiple fringes and average left and right positions |
| Error in measuring screen distance | The denominator in the wavelength calculation is incorrect | All wavelength values shift in the same direction | Measure from the slit plane to the screen plane |
| Error in the nominal slit separation | Affects wavelength proportionally | Produces a systematic error throughout the measurement | Use a calibrated value or verify with another slit |
| Optical axis not perpendicular to the screen | Left and right fringe spacings differ | Interference fringes become asymmetric | Align the laser, slits, and screen face-on |
| Laser not centered on the slits | The light intensities through the two slits become unequal | Fringe contrast decreases | Adjust the incident position and angle |
| Apparatus vibration | Fringe positions fluctuate with time | Fringes appear blurred | Use a stable bench and do not touch the apparatus during measurement |
| Ambient light | Dark fringes appear brighter | Fringe contrast decreases | Darken the room or shield the apparatus from light |
| Diffraction due to slit width | The overall fringe brightness varies with position | Outer fringes become darker | Account for the diffraction envelope and measure near the center |
| Limit of the small-angle approximation | The position formula deviates for high-order outer fringes | Higher orders deviate more from a linear relationship | Use fringes near the center or calculate with exact trigonometric functions |
| Laser spectral width | The light is not perfectly monochromatic | High-order fringes may become less distinct | Use a stable monochromatic laser |
Why Bright and Dark Fringes Appear
The light from the two slits travels different distances depending on the position on the screen. If this path difference is an integer multiple of the wavelength, crests overlap crests and troughs overlap troughs, producing constructive interference and a bright fringe.
If the path difference is an odd multiple of half a wavelength, crests overlap troughs, producing destructive interference and a dark fringe.
Why the Fringe Spacing Is Nearly Constant
Within the range where the small-angle approximation is valid, the bright-fringe position is proportional to the order m. Therefore, the difference in position between adjacent bright fringes is constant, and nearly equally spaced interference fringes are observed.
Why Moving the Screen Farther Away Spreads the Fringes
The fringe spacing is given by Δx = λL/d. Therefore, if the wavelength and slit separation are constant, the fringe spacing increases in proportion to the screen distance.
Moving the screen farther away makes the fringes easier to measure, but the overall brightness decreases because the light spreads out.
Why a Smaller Slit Separation Produces Wider Fringes
Fringe spacing is inversely proportional to slit separation. The closer the two slits are, the larger the angle required to produce the same optical path difference, so the fringe spacing on the screen becomes wider.
Why the Outer Fringes Become Darker
Because real double slits have finite width, diffraction also occurs at each individual slit. The fine double-slit interference fringes appear within a broader intensity distribution caused by single-slit diffraction.
As a result, the central region is brightest and the overall brightness of the interference fringes decreases toward the outside.
Example of How to Write the Results
Red laser light was incident on a double slit with a slit separation of 0.250 mm, and the interference fringes formed on a screen 1.50 m away were observed.
When the bright-fringe positions were measured from the central bright fringe to the fifth order on both sides, the fringe positions were approximately proportional to the order, and the interference fringes were nearly equally spaced. The distance spanning 10 fringes was 39.0 mm, giving a fringe spacing of 3.90 mm.
The wavelength of the laser light calculated from the double-slit equation was 650 nm, matching the nominal value of 650 nm. In addition, increasing the screen distance caused the fringe spacing to increase proportionally.
Points to Connect to the Discussion
- Were the bright-fringe positions proportional to the order?
- Were the interference fringes symmetric and equally spaced on both sides?
- Did the measured wavelength agree with the nominal wavelength of the light source?
- Were screen distance and fringe spacing proportional?
- Can the inverse relationship between slit separation and fringe spacing be explained?
- What was the benefit of measuring across multiple fringes?
- Can the darkening of outer fringes be related to diffraction?
- If the left and right fringe positions differed, what caused the difference?
- Was the small-angle approximation valid over the measured range?
- Did optical-axis misalignment, ambient light, vibration, or slit contamination affect the results?
Discussion Example
In this experiment, red laser light was passed through a double slit and the resulting interference fringes on a screen were observed. The wavelength of the laser light was also determined from the fringe spacing.
With a slit separation of 0.250 mm and a screen distance of 1.50 m, the interference fringe spacing was 3.90 mm. Substituting this value into the double-slit equation gave a wavelength of 650 nm, which agreed with the nominal value of 650 nm.
The bright and dark fringes on the screen were produced because light from the two slits overlapped and underwent constructive or destructive interference depending on the optical path difference. A bright fringe occurs where the path difference is an integer multiple of the wavelength, while a dark fringe occurs where it is an odd multiple of half a wavelength.
The distance from the center to each bright fringe was approximately proportional to the fringe order. This confirms that, within the range where the small-angle approximation is valid, the bright-fringe positions follow xm = mλL/d.
When the screen distance was increased from 1.00 m to 1.75 m, the fringe spacing increased from 2.60 mm to 4.54 mm. Because fringe spacing is proportional to screen distance, the experimental results agreed with the theory.
The main sources of measurement error include error in reading the centers of bright fringes, error in measuring the distance from the slits to the screen, error in the nominal slit separation, and misalignment of the optical axis.
In particular, each bright fringe has a finite width, making it difficult to define its center as a single exact point. Therefore, rather than measuring only one adjacent fringe interval, the distance spanning 10 fringes was measured and divided by 10, reducing the influence of a single reading error on the calculated fringe spacing.
A slight difference was observed between the left and right bright-fringe positions. Possible causes include the laser beam not being incident perpendicular to the double slit or the screen being tilted relative to the optical axis. Averaging the left and right positions can reduce this effect to some extent.
The outer interference fringes were darker than those near the center. This is because single-slit diffraction occurs due to the finite width of each slit, causing the brightness of the double-slit interference fringes to vary according to the diffraction envelope.
For high-order fringes, the difference between the position predicted by the small-angle approximation and the actual value may become larger. Therefore, fringes near the center should be used for wavelength calculations, or exact trigonometric relations should be used when necessary.
To improve measurement accuracy, the centers of the laser, double slit, and screen should be aligned on the same straight line, and the screen surface should be perpendicular to the optical axis. It is also effective to darken the room, avoid apparatus vibration, repeat the measurements, and calculate an average value.
These results confirm that light exhibits constructive and destructive interference through superposition, that bright-fringe position is proportional to fringe order, and that the wavelength of light can be determined from the interference fringe spacing.
Discussion Example When the Measured Wavelength Is Larger Than the Nominal Value
If the measured wavelength is larger than the nominal value, possible causes include reading the fringe spacing as wider than it actually was, using a slit-separation value larger than the actual value, or measuring the screen distance as shorter than it actually was. If the screen was tilted relative to the optical axis, the apparent fringe spacing could also become wider.
Discussion Example When the Interference Fringes Are Unclear
Possible reasons for unclear interference fringes include uneven illumination of the two slits by the laser, strong ambient light, apparatus vibration, or dirt and scratches on the slits. If the intensities of the two waves differ greatly, the light does not cancel sufficiently even at dark fringes, reducing fringe contrast.
Summary
In a double-slit interference experiment, light from the two slits overlaps and produces bright and dark interference fringes on the screen.
Fringe spacing is proportional to the wavelength of light and the screen distance, and inversely proportional to the slit separation. By measuring the fringe spacing, slit separation, and screen distance, the wavelength of light can be determined.
In the discussion, it is important to relate optical path difference, constructive and destructive interference, the small-angle approximation, the diffraction envelope, optical-axis alignment, fringe-center readings, and screen distance.
