Young's Double Slit Experiment: Videos & Practice Problems

Young's double slit experiment demonstrates light's wave nature through diffraction and interference. When collimated light passes through two slits, it creates a diffraction pattern of alternating bright (constructive interference) and dark (destructive interference) fringes on a screen. The positions of these fringes can be calculated using the equations: sin(θ) = mλd for bright fringes and sin(θ) = n+1λd for dark fringes, where m and n are indexing numbers, λ is the wavelength, and d is the slit separation.

Young's Double Slit Experiment

Young's double slit experiment is a fundamental demonstration of the wave nature of light, showcasing how light rays can interfere with one another after passing through two closely spaced slits. Initially, it was believed that a beam of collimated light directed at the double slit would produce a single bright spot on a screen. However, the actual outcome reveals a diffraction pattern characterized by alternating bright and dark fringes, resulting from the interference of light waves.

When light waves pass through the slits, they spread out and travel in various directions, leading to constructive and destructive interference. Constructive interference occurs when the peaks of two waves align, resulting in bright fringes, while destructive interference happens when a peak aligns with a trough, creating dark fringes. This alternating pattern of brightness is a direct consequence of diffraction, which causes the initially collimated light to disperse as it encounters the slits.

The positions of the bright fringes can be calculated using the formula:

$\sin(\theta) = \frac{m \lambda}{d}$

In this equation, $\theta$ represents the angle at which the bright fringe occurs, $m$ is the indexing number (0, 1, 2, 3, etc.), $\lambda$ is the wavelength of the light, and $d$ is the separation between the two slits. The dark fringes are determined by a similar formula:

$\sin(\theta) = \frac{(n + \frac{1}{2}) \lambda}{d}$

where $n$ is the indexing number for the dark fringes.

For example, consider a 650 nanometer laser directed through a double slit with a separation of 10 millimeters. To find the angle of the fourth bright fringe, we identify that this corresponds to $m = 3$. Plugging the values into the bright fringe formula gives:

$\sin(\theta_3) = \frac{3 \times 650 \times 10^{-9}}{10 \times 10^{-3}}$

Calculating this results in a very small angle, approximately 0.011 degrees, which is typical for such experiments due to the small scale of the angles involved.

To determine the distance from the central bright fringe to the fourth bright fringe on a screen located 2.8 meters away, we can use trigonometry. The relationship can be expressed as:

$\tan(\theta) = \frac{y}{L}$

where $y$ is the vertical distance to the fringe and $L$ is the distance from the slits to the screen. Rearranging gives:

$y = L \tan(\theta)$

Substituting the known values leads to a calculated distance of approximately 0.54 millimeters, illustrating how even small angles can result in minimal displacement on a distant screen.

Overall, Young's double slit experiment not only highlights the wave properties of light but also provides a framework for understanding interference patterns through mathematical analysis.

A 450 nm laser shines light through a double slit of 0.2 mm separation. If a screen is placed 4 m behind the double slit, how wide are the bright fringes of the diffraction pattern?

• A. 9.0 mm
• B. 4.5 mm
• C. 2.2 mm
• D. 0.055 mm

Answer: (A)

Unknown Wavelength of Laser through Double Slit

In Young's double slit experiment, we explore the behavior of monochromatic light, which refers to light of a single wavelength, typically emitted by lasers. In this scenario, a laser shines light through a double slit with a separation of 0.2 millimeters, and a screen is positioned 5.5 meters behind the slits. The angular separation between each bright fringe is measured to be 0.15 degrees.

To find the wavelength of the laser light, we start by understanding the relationship between the angle of the bright fringes and the wavelength. The angular position of the bright fringes can be described using the formula:

$m^{\lambda }=dsin\left(\theta \right)$

Here, m represents the order of the fringe (with m = 1 for the first bright fringe), λ is the wavelength, d is the slit separation, and θ is the angle corresponding to the fringe. For the first bright fringe, we set m = 1 and use the given angle of 0.15 degrees.

We convert the angle from degrees to radians for calculation purposes, but for small angles, the sine of the angle can be approximated as the angle itself in radians. Thus, we can express the wavelength as:

$\lambda =dsin(\mathrm{\theta \; <mo>)</mo>}$

Substituting the values, we have:

$\lambda =0.2\; mmsin(0.15°)$

Converting 0.2 millimeters to meters gives us 0.2 x 10^-3 meters. After calculating, we find the wavelength to be approximately 5.24 x 10^-7 meters. To express this in nanometers, we shift the decimal point two places to the right, resulting in a wavelength of 524 nanometers.

This wavelength falls within the visible spectrum, which ranges from approximately 450 nanometers (violet) to 750 nanometers (red). Understanding these concepts is crucial for grasping the principles of wave interference and the nature of light.

Here’s what students ask on this topic:

What is Young's double slit experiment and what does it demonstrate?

Young's double slit experiment is a fundamental demonstration of the wave nature of light. In this experiment, collimated light passes through two closely spaced slits and creates a pattern of alternating bright and dark fringes on a screen. This pattern, known as a diffraction pattern, results from the interference of light waves. Constructive interference occurs where the light waves are in phase, producing bright fringes, while destructive interference occurs where the waves are out of phase, producing dark fringes. The experiment provides strong evidence for the wave theory of light, showing that light can exhibit properties of both waves and particles.

How do you calculate the positions of bright and dark fringes in Young's double slit experiment?

The positions of bright and dark fringes in Young's double slit experiment can be calculated using specific equations. For bright fringes (constructive interference), the equation is:

$\sin \left(\theta \right)=m\lambda /d$

where m is an integer (0, 1, 2, ...), λ is the wavelength of the light, and d is the separation between the slits. For dark fringes (destructive interference), the equation is:

$\sin \left(\theta \right)=(n+1/2)\lambda /d$

where n is an integer (0, 1, 2, ...). These equations help determine the angles at which the bright and dark fringes appear on the screen.

What is the significance of the indexing number in Young's double slit experiment?

The indexing number in Young's double slit experiment is crucial for identifying the positions of the bright and dark fringes. For bright fringes, the indexing number m (0, 1, 2, ...) indicates the order of the fringe, with m = 0 representing the central bright fringe. For dark fringes, the indexing number n (0, 1, 2, ...) helps locate the dark fringes between the bright ones. These numbers are essential for applying the equations:

$\sin \left(\theta \right)=m\lambda /d$

for bright fringes and

$\sin \left(\theta \right)=(n+1/2)\lambda /d$

for dark fringes, where λ is the wavelength and d is the slit separation.

Why are the angles in Young's double slit experiment typically very small?

The angles in Young's double slit experiment are typically very small because the separation between the slits (d) is usually much larger than the wavelength of the light (λ). This results in small values for the sine of the angle (sin(θ)) in the equations:

$\sin \left(\theta \right)=m\lambda /d$

for bright fringes and

$\sin \left(\theta \right)=(n+1/2)\lambda /d$

for dark fringes. Since sin(θ) is small, the angles θ themselves are also small. This small-angle approximation simplifies the mathematical analysis and is a common assumption in the study of diffraction and interference patterns.

How does the separation between the slits affect the diffraction pattern in Young's double slit experiment?

The separation between the slits (d) in Young's double slit experiment significantly affects the diffraction pattern. A larger slit separation results in fringes that are closer together, while a smaller slit separation causes the fringes to spread further apart. This relationship is evident in the equations:

$\sin \left(\theta \right)=m\lambda /d$

for bright fringes and

$\sin \left(\theta \right)=(n+1/2)\lambda /d$

for dark fringes. As d increases, the angles θ for both bright and dark fringes decrease, leading to a more compact pattern. Conversely, decreasing d increases the angles θ, resulting in a more spread-out pattern. This demonstrates the inverse relationship between slit separation and fringe spacing.