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What is Fringe Width?
Grade Level:
Class 12
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Definition
What is it?
Fringe width is the distance between the centres of two consecutive bright fringes (or two consecutive dark fringes) in an interference pattern. It tells us how spread out the bright and dark bands are when light waves meet.
Simple Example
Quick Example
Imagine you're watching a cricket match on a big screen, and due to some issue, you see two identical images slightly shifted. The distance between the centre of one player in the first image and the same player in the next image, if they were repeating, would be like fringe width. It's the gap between similar repeating patterns.
Worked Example
Step-by-Step
Let's calculate the fringe width for a Young's Double Slit Experiment.
Given:
- Wavelength of light (lambda) = 600 nm = 600 x 10^-9 meters
- Distance between slits (d) = 0.2 mm = 0.2 x 10^-3 meters
- Distance between slits and screen (D) = 1 meter
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Step 1: Recall the formula for fringe width (beta).
beta = (lambda * D) / d
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Step 2: Substitute the given values into the formula.
beta = (600 x 10^-9 m * 1 m) / (0.2 x 10^-3 m)
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Step 3: Calculate the numerator.
600 x 10^-9 * 1 = 600 x 10^-9
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Step 4: Perform the division.
beta = (600 x 10^-9) / (0.2 x 10^-3)
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Step 5: Simplify the powers of 10.
beta = (600 / 0.2) x (10^-9 / 10^-3)
beta = 3000 x 10^(-9 - (-3))
beta = 3000 x 10^(-9 + 3)
beta = 3000 x 10^-6 meters
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Step 6: Convert to a more common unit, like millimeters.
beta = 3 x 10^3 x 10^-6 meters
beta = 3 x 10^-3 meters
beta = 3 mm
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The fringe width (beta) is 3 mm.
Why It Matters
Understanding fringe width is crucial in fields like optical engineering and sensor technology. It helps engineers design better optical instruments, from high-resolution microscopes used in biotechnology to advanced sensors in space technology. Scientists working on new display technologies for EVs or advanced medical imaging also use this concept to control light patterns precisely.
Common Mistakes
MISTAKE: Confusing fringe width with the width of a single bright or dark fringe. | CORRECTION: Fringe width is the distance between the *centres* of two *consecutive* bright or dark fringes, not the width of just one.
MISTAKE: Using inconsistent units in the formula (e.g., meters for wavelength, millimeters for slit distance). | CORRECTION: Always convert all measurements (wavelength, slit distance, screen distance) to a consistent unit, usually meters, before applying the formula.
MISTAKE: Forgetting that the formula for fringe width is for Young's Double Slit Experiment specifically. | CORRECTION: The formula beta = (lambda * D) / d is specific to interference patterns from two coherent sources. Other diffraction or interference patterns might have different ways to calculate fringe spacing.
Practice Questions
Try It Yourself
QUESTION: If the distance between the slits and the screen (D) is doubled, how does the fringe width change, assuming all other factors remain constant? | ANSWER: The fringe width will also double.
QUESTION: In a Young's Double Slit Experiment, the fringe width is 2 mm. If the wavelength of light used is 500 nm and the distance between the slits and screen is 1.5 m, what is the distance between the two slits? | ANSWER: d = 0.375 mm
QUESTION: A student observes an interference pattern where the 5th bright fringe is 10 mm away from the central bright fringe. If the distance between the slits and screen is 1.2 m and the slit separation is 0.4 mm, calculate the wavelength of light used. (Hint: The position of the nth bright fringe is n * beta). | ANSWER: lambda = 666.67 nm (approx)
MCQ
Quick Quiz
Which of the following factors, if increased, would lead to an increase in fringe width?
Distance between the slits (d)
Wavelength of light (lambda)
Frequency of light
Refractive index of the medium
The Correct Answer Is:
B
Fringe width (beta) is directly proportional to the wavelength (lambda). So, increasing the wavelength will increase the fringe width. It is inversely proportional to the distance between slits (d), and not directly affected by frequency or refractive index in the standard formula.
Real World Connection
In the Real World
Fringe width is important in optical sensors used in automated manufacturing, like those in car factories or even for checking the quality of mobile phone screens. Engineers use interference patterns and measure fringe widths to detect tiny defects or measure very small distances with high precision. For example, ISRO scientists might use similar principles to calibrate instruments for satellite imaging.
Key Vocabulary
Key Terms
INTERFERENCE: When two or more waves meet and combine to form a new wave of greater or lesser amplitude. | FRINGE: The bright or dark bands observed in an interference pattern. | WAVELENGTH: The distance between two consecutive crests or troughs of a wave. | COHERENT SOURCES: Light sources that emit waves with a constant phase difference and the same frequency. | DIFFRACTION: The bending of waves as they pass around an obstacle or through an opening.
What's Next
What to Learn Next
Now that you understand fringe width, you can explore Young's Double Slit Experiment in more detail, which is where this concept comes from. You'll learn how to derive the formula and understand the conditions required for clear interference patterns. Keep up the great work!
