Young's Double Slit Experiment

Young's Double Slit Experiment

Vishal kumarUpdated on 02 Jul 2025, 06:25 PM IST

Young's Double Slit Experiment is a cornerstone of quantum physics that elegantly demonstrates the wave-particle duality of light. Conducted by Thomas Young in 1801, the experiment involves shining a coherent light source through two closely spaced slits and observing the resulting pattern on a screen. Instead of forming two distinct lines, as expected for particles, the light creates an intricate pattern of bright and dark fringes, indicating interference—a property characteristic of waves. This surprising outcome challenges our intuitive understanding of nature, showing that particles like photons can exhibit both particle-like and wave-like behaviours. In real life, this experiment's principles can be seen in phenomena such as the colourful patterns in soap bubbles, the ripples created when two stones are thrown into a pond, or even in modern technology like holography and quantum computing. In this article, we will discuss the concept of Young's double-slit experiment, assumptions, and solved examples for better concept clarity.

Young's Double Slit Experiment
Young's Double Slit Experiment

Young's Double-Slit Experiment

This experiment is performed by British physicist Thomas Young. He used an arrangement as shown below. In this he used a monochromatic source of light S . He made two pinholes S1 and S2 (very close to each other) on an opaque screen as shown in the figure Each source can be considered as a source of coherent light source.

So, we can see that the monochromatic light source ‘s’ kept at a considerable distance from two slits s1 and s2. The arrangement is such that the S is equidistant from S1 and S2. S1 and S2 behave as two coherent sources, as both are derived from S.

Let d be the distance between two coherent sources A and B having wavelength λ. A screen XY is placed parallel to an opaque screen at a distance D. O is a point on the screen equidistant from A and B. P is a point at a distance x from O.

From the above figure, we can see that the waves from A and B meet at P. It may be in phase or out of phase depending upon the path difference between the two waves, which we will calculate.

Draw AM perpendicular to BP
The path difference $\delta=\mathrm{BP}-\mathrm{AP}$
As we can see that, $\mathrm{AP}=\mathrm{MP}$
$$
\delta=\mathrm{BP}-\mathrm{AP}=\mathrm{BP}-\mathrm{MP}=\mathrm{BM}
$$

In right angled $\mathrm{ABM}, \quad \mathrm{BM}=\mathrm{d} \sin \theta$ if $\theta$ is small,
$$
\sin \theta=\theta
$$

The path difference $\delta=\theta \cdot d$
In right angled triangle $\mathrm{COP}, \quad \tan \theta=\mathrm{OP} / \mathrm{CO}=\mathrm{X} / \mathrm{D}$
For small values of $\theta, \tan \theta=\theta$
Thus, the path difference $\delta=\mathrm{xd} / \mathrm{D}$
So, the path difference is $=\frac{x d}{D}$

The Assumption in this Experiment

1. D> d: Since D > > d, the two light rays are assumed to be parallel.

2. d/λ >> 1: Often, d is a fraction of a millimeter and λ is a fraction of a micrometer for visible light.

For Bright Fringes

By the principle of interference, the condition for constructive interference is the path difference $=\mathrm{n} \lambda$
$$
\frac{x d}{D}=n \lambda
$$

Here, $n=0,1,2 \ldots \ldots$ indicate the order of bright fringes
So, $x=\left(\frac{n \lambda D}{d}\right)$
This equation gives the distance of the $n^{\text {th }}$ bright fringe from the point $O$.

For Dark fringes

By the principle of interference, the condition for destructive interference is the path difference = $\frac{(2 n-1) \lambda}{2}$

Here, n = 1,2,3 … indicates the order of the dark fringes.

so, $x=\frac{(2 n-1) \lambda D}{2 d}$

The above equation gives the distance of the nth dark fringe from point O.

So, we can say that the alternately dark and bright fringe will be obtained on either side of the central bright fringe.

Band Width (β)

The distance between any two consecutive bright or dark bands is called bandwidth. The bandwidth of the light source plays a crucial role in determining the clarity and visibility of the interference pattern observed on the screen.

Take the consecutive dark or bright fringe

$\begin{aligned} x_{n+1}-x_n & =\frac{(n+1) \lambda D}{d}-\frac{(n) \lambda D}{d} \\ x_{n+1}-x_n & =\frac{\lambda D}{d} \\ \beta & =\frac{\lambda D}{d}\end{aligned}$

Angular Fringe Width

Angular fringe width can be observed in the diffraction patterns of light through narrow apertures, where the angle between the bright fringes corresponds to the angular fringe width. It is an essential parameter in designing optical instruments and understanding the behaviour of light in various contexts.

$\theta=\frac{\beta}{D}=\frac{\lambda D / d}{D}=\frac{\lambda}{d}$



Solved Examples Based on Young's Double Slit Experiment

Example 1: In Young's experiment, the interfering has amplitudes in the ratio 3:2, and then ratios of amplitudes between bright and dark fringes are:

1) 5:1

2) 9:4

3) 7:1

4) 49:1

Solution:

The resultant amplitude of two waves

$A=\sqrt{A_1^2+A_2^2+2 A_1 A_2 \cos \theta}$
wherein

$A_{1}=$ amplitude of wave 1

$A_{2}=$ amplitude of wave 2

$\theta =$ phase difference

We have to obtain the ratio

$\frac{A_{\max }}{A_{\min }}=\frac{A_1+A_2}{A_1-A_2}$

and also the corresponding ratio of intensities

$\frac{I_{\max }}{I_{\min }}=\frac{\left(A_1+A_2\right)^2}{\left(A_1-A_2\right)^2}$

but $\frac{A_1}{A_2}=\frac{3}{2}$

By correspond and divide

$\frac{A_1+A_2}{A_1-A_2}=\frac{3+2}{3-2}=5$

Hence,

$\frac{A_{\max }}{A_{\min }}=5 \quad \frac{I_{\max }}{I_{\min }}=25$

Hence, the answer is the option (1).

Example 2: In Young's double slit experiment, the path difference, at a certain point on the screen between two interfering waves is $\frac{1}{8} t h$ of the wavelength. The ratio of the intensity at this point to that at the center of a bright fringe is close to:

1)0.80

2)0.94

3)0.85

4)0.74

Solution

$$
\begin{aligned}
& \Delta x=\frac{\lambda}{8} \\
& \Delta \phi=\left(\frac{2 \pi}{\lambda}\right) \frac{\lambda}{8}=\frac{\pi}{4} \\
& I=I_1+I_2+2 \sqrt{I_1 I_2} \cos \theta
\end{aligned}
$$

Putting $I_1$ and $I_2=I_o$

we get $\Rightarrow I=I_0+I_0+2 \sqrt{I_0 I_0} \cos \phi=4 I_0 \cos ^2 \frac{\phi}{2}$

At the centre $I_c=4 I_0$

and at that point $I=4 I_o \cos ^2\left(\frac{\pi}{8}\right)=I_c \cos ^2\left(\frac{\pi}{8}\right)$

$\begin{aligned} & \frac{I}{I_c}=\cos ^2\left(\frac{\pi}{8}\right) \\ & \approx 0.85\end{aligned}$

Hence, the answer is the option (3).

Example 3: Two silts in Young’s experiment have width in the ratio 1:25. The ratio of intensity at maxima and minima in the interference pattern $\frac{I_{\max }}{I_{\min }}$ is:

1) $\frac{9}{4}$
2) $\frac{3}{2}$
3) $\frac{121}{49}$
4) $\frac{5}{1}$

Solution

Maximum amplitude & Intensity

When $\theta=0,2 \pi---2 n \pi$
wherein

$\begin{aligned} & A_{\max }=A_1+A_2 \\ & I_{\max }=\left(\sqrt{I_1}+\sqrt{I_2}\right)^2 \\ & \frac{I_1}{I_2}=\frac{1}{25} \quad \text { OR } \quad \frac{I_2}{I_1}=\frac{25}{1} \\ & \frac{I_{\max }}{I_{\min }}=\left(\frac{\sqrt{I_2}+\sqrt{I_1}}{\sqrt{I_2}-\sqrt{I_1}}\right)^2 \quad \frac{I_{\max }}{I_{\min }}=\left(\frac{\sqrt{I_2}+\sqrt{I_1}}{\sqrt{I_2}-\sqrt{I_1}}\right)^2=\left(\frac{\sqrt{\frac{I_2}{I_1}}+1}{\sqrt{I_2}}\right)^2 \\ & \frac{I_{\max }}{I_{\min }}=\left(\frac{5+1}{5-1}\right)^2=\frac{9}{4}\end{aligned}$

Hence, the answer is the option (1).

Example 4: Two monochromatic light beams of intensity 16 and 9 units are interfering. The ratio of intensities of bright and dark parts of the resultant pattern is :

1) $\frac{16}{9}$
2) $\frac{4}{3}$
3) $\frac{7}{1}$
4) $\frac{49}{1}$

Solution:

Maximum amplitude & Intensity

When $\theta=0,2 \pi---2 n \pi$
wherein

$\begin{aligned} & A_{\text {max }}=A_1+A_2 \\ & I_{\max }=\left(\sqrt{I_1}+\sqrt{I_2}\right)^2\end{aligned}$

Minimum amplitude & Intensity

$\begin{aligned} & \theta=(2 n+1) \pi \\ & A_{\min }=A_1-A_2 \\ & I_{\min }=\left(\sqrt{I_1}-\sqrt{I_2}\right)^2 \\ & \frac{I_{\max }}{I_{\min }}=\left(\frac{\sqrt{I}_1+\sqrt{I}_2}{\sqrt{I_1}-\sqrt{I_2}}\right)^2=\left(\frac{4+3}{4-3}\right)^2=49: 1\end{aligned}$

Hence, the answer is the option (4).

Example 5: In Young's double slit experiment, the ratio of the slit's width is 4:1 The ratio of the intensity of maxima to minima, close to the central fringe in the screen, will be:

1) $25: 9$
2) $9: 1$
3) $4: 1$
4) $(\sqrt{3+1})^4: 16$

Solution:

$\begin{aligned} & \frac{I_1}{I_2}=\frac{4}{1} \\ & \frac{I_{\max }}{I_{\min }}=\frac{\left(\sqrt{I_1}+\sqrt{I_2}\right)^2}{\left(\sqrt{I_1}-\sqrt{I_2}\right)^2}=\left(\frac{\sqrt{\frac{I_1}{I_2}}+1}{\sqrt{\frac{I_1}{I_2}}-1}\right)^2 \\ & \Rightarrow \frac{I_{\max }}{I_{\min }}=\left(\frac{\sqrt{4}+1}{\sqrt{4}-1}\right)^2=\left(\frac{2+1}{2-1}\right)^2=\left(\frac{3}{1}\right)^2 \\ & \Rightarrow \frac{I_{\max }}{I_{\min }}=\left(\frac{9}{1}\right)\end{aligned}$

Hence, the answer is the option (2).

Summary

Young's Double Slit Experiment, conducted by Thomas Young in 1801, demonstrates the wave-particle duality of light by showing an interference pattern when coherent light passes through two closely spaced slits. This phenomenon, which produces alternating bright and dark fringes, arises from constructive and destructive interference of waves. The experiment's principles can be observed in various real-world phenomena and have significant implications in fields like holography and quantum computing. The article discusses key concepts, assumptions, and solved examples, emphasizing the importance of parameters like fringe width and intensity ratios in understanding interference patterns.

Frequently Asked Questions (FAQs)

Q: What is the role of the single slit before the double slits in some versions of the experiment?
A:
In some versions of Young's Double Slit Experiment, a single slit is placed before the double slits. This single slit serves several purposes:
Q: How does Young's Double Slit Experiment demonstrate the principle of least time?
A:
Young's Double Slit Experiment indirectly demonstrates Fermat's Principle of Least Time, which states that light takes the path that requires the least time. In the experiment, the bright fringes occur where the path difference between waves from the two slits is a whole number of wavelengths. This corresponds to paths where the waves arrive in phase, which aligns with the principle of least time. The interference pattern thus reflects the optimal paths for light travel, consistent with Fermat's principle.
Q: What happens to the interference pattern if the screen is tilted?
A:
If the screen in Young's Double Slit Experiment is tilted, the interference pattern becomes distorted. The fringes appear closer together on the side of the screen that's farther from the slits and farther apart on the side that's closer. This is because the path difference between waves from the two slits changes non-uniformly across the tilted screen. The central maximum shifts to where the screen is equidistant from both slits. This effect can be used to precisely align the screen perpendicular to the incoming light.
Q: How does the concept of temporal coherence apply to Young's Double Slit Experiment?
A:
Temporal coherence in Young's Double Slit Experiment refers to how long the light waves maintain a consistent phase relationship over time. High temporal coherence is necessary for clear interference patterns. It determines the maximum path difference over which interference can occur (coherence length). Light sources with high temporal coherence, like lasers, produce sharp, well-defined fringes over a large area. Sources with low temporal coherence, like white light, produce fewer visible fringes or colored fringes due to the mixing of different wavelengths.
Q: What is the significance of the Fresnel number in Young's Double Slit Experiment?
A:
The Fresnel number is a dimensionless quantity that helps determine whether the experiment is in the near-field (Fresnel) or far-field (Fraunhofer) diffraction regime. It's defined as F = a²/(λL), where a is the slit width, λ is the wavelength, and L is the distance to the screen. When F is much less than 1, the experiment is in the far-field regime, where the standard Young's interference pattern is observed. As F approaches or exceeds 1, near-field effects become significant, complicating the interference pattern.
Q: What is the role of coherence length in Young's Double Slit Experiment?
A:
Coherence length is the maximum path difference over which interference can occur. In Young's Double Slit Experiment, it determines the maximum number of observable fringes. If the path difference between waves from the two slits exceeds the coherence length, the interference pattern becomes unclear or disappears. Light sources with longer coherence lengths (like lasers) produce clearer, more extensive interference patterns than those with shorter coherence lengths (like ordinary lamps).
Q: What happens to the interference pattern if the slits are not identical?
A:
If the slits are not identical (e.g., different widths or shapes), the interference pattern becomes asymmetrical. The fringe spacing remains the same, but the intensity distribution changes. One set of fringes may become brighter than the other, or the overall pattern may shift slightly. This is because the diffraction patterns from each slit are no longer identical, affecting how they interfere.
Q: How does the thickness of the double slit barrier affect the experiment?
A:
The thickness of the double slit barrier can affect the experiment by influencing the amount of light that passes through the slits. If the barrier is too thick relative to the slit width, it can cause additional diffraction effects or reduce the overall intensity of light reaching the screen. Ideally, the barrier should be thin enough to minimize these effects while still effectively separating the two slits.
Q: What is the Fraunhofer condition in relation to Young's Double Slit Experiment?
A:
The Fraunhofer condition in Young's Double Slit Experiment refers to the requirement that the screen be sufficiently far from the slits for the interference pattern to be clearly observed. Mathematically, it's expressed as L >> d²/λ, where L is the distance to the screen, d is the slit separation, and λ is the wavelength. When this condition is met, the light rays reaching any point on the screen are effectively parallel, simplifying the analysis of the interference pattern.
Q: How does polarization affect Young's Double Slit Experiment?
A:
Polarization doesn't directly affect the interference pattern in Young's Double Slit Experiment when using a single polarized light source. However, if you use two different polarized light sources for each slit, the interference pattern can be affected. If the polarizations are perpendicular, no interference occurs. As you rotate one polarizer, the interference pattern gradually appears, demonstrating that interference only occurs between waves with the same polarization.