Assertion (A) :- Interference pattern is made by using blue light instead of red light, the fringes

Assertion (A) :- Interference pattern is made by using blue light instead of red light, the fringes becomes narrower.
Reason (R) :- In Young's double slit experiment, fringe width is given by relation β = λD/d
(a) Both (A) and (R) are correct but (R) is not the correct explanation of (A)
(b) (A) is correct but (R) is incorrect
(c) (A) is incorrect but (R) is correct
(d) Both (A) and (R) are correct and (R) is the correct explanation of (A)
In this video, we will explore the fascinating concept of *interference* in wave optics 🌊, specifically focusing on how the wavelength of light influences the *fringe width* in **Young’s double-slit experiment**. This experiment, a cornerstone in wave optics, demonstrates the wave nature of light 🌟, where two coherent light sources interfere with each other to create a pattern of alternating bright and dark fringes on a screen. But what happens when we change the color of light, for example, from red to blue? The answer lies in understanding the relationship between wavelength and fringe width, a key concept for your NEET and JEE physics preparations.
*Interference and Fringe Width* 🔬:
When we perform **Young's double-slit experiment**, the interference pattern that emerges is highly dependent on the wavelength (λ) of the light used. The fringe width (β), which is the distance between adjacent bright or dark fringes, is given by the formula:
*β = λD/d*
Where:
*λ* is the wavelength of the light used,
*D* is the distance from the slits to the screen,
*d* is the distance between the slits.
The key takeaway from this formula is that the fringe width is *directly proportional* to the *wavelength* of the light used. This means that if the wavelength increases, the fringe width becomes **wider**, and if the wavelength decreases, the fringe width becomes **narrower**.
Now, let’s apply this theory to real-life examples. When *blue light* (which has a shorter wavelength) is used in the experiment, the fringe width becomes **narrower**. This is in contrast to **red light**, which has a longer wavelength and thus produces **wider fringes**. This phenomenon is essential to understand for competitive exams like NEET and JEE, where questions related to interference patterns often appear.
**The Relationship Between Wavelength and Interference**:
The concept of fringe width directly relates to the wavelength of light. Light behaves as both a particle and a wave, and when it passes through two slits, the waves interfere with each other. This interference can be constructive or destructive:
*Constructive interference* occurs when the path difference between the two waves is an integer multiple of the wavelength, resulting in bright fringes.
*Destructive interference* happens when the path difference is an odd multiple of half the wavelength, resulting in dark fringes.
The formula for fringe width, *β = λD/d**, shows how **λ* plays a crucial role in determining the spacing between the fringes. By using *blue light* with a shorter wavelength compared to red light, the fringes become closer together, making the pattern more compact.
This relationship between the wavelength and fringe width provides a powerful tool to explain and predict the behavior of light in various interference experiments. Whether you're preparing for NEET or JEE, understanding how different wavelengths affect the fringe pattern can help you solve complex problems involving light and optics.
**Blue Light vs. Red Light**:
To summarize the differences:
*Blue light* has a shorter wavelength (around 450-495 nm).
*Red light* has a longer wavelength (around 620-750 nm).
When we replace red light with blue light in the *Young’s double-slit experiment**, the **fringe width* decreases. This is because blue light has a shorter wavelength, and according to the formula *β = λD/d*
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