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In a Young's double slit experiment, the source is white light. One of the holes is covered by a red filter and another by a blue filter. In this case (a) there should be no interference fringe (b) there should be an interference pattern for red mixing with one for blue (c) there should be altemate interference patterns of red and blue (d) None of the above

Short Answer

Expert verified
(d) None of the above.

Step by step solution

01

Understand the Experiment

A Young's double slit experiment involves light passing through two closely spaced slits to create an interference pattern on a screen. Each slit acts as a source of light waves that spread out and combine to form the pattern, showing constructive and destructive interference.
02

Analyze the Effects of Filters

In this scenario, a red filter covers one slit, allowing only red light through, while a blue filter covers the other slit, allowing only blue light through. These filters ensure that each slit emits light of different wavelengths.
03

Determine Possibility of Interference

For interference to occur, the light waves need to be coherent, meaning they must have a constant phase relationship, which is typical when they are of the same wavelength. Here, one slit emits red light and the other emits blue light, making them incoherent.
04

Evaluate the Options Given

(a) There should be no interference fringe: This suggests no visible pattern due to incoherence. (b) An interference pattern for red mixing with one for blue: This implies mixture, which isn't possible due to incoherence. (c) Alternate patterns of red and blue: Predicts visible alternating patterns, which can't happen with incoherent sources. None of the choices describe the situation correctly. (d) None of the above: Evaluating previous steps indicates that none accurately describe what happens.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Interference Pattern
An interference pattern is a series of bright and dark bands or lines created when waves overlap, such as light waves. This happens when light from two sources, like the slits in Young's double slit experiment, overlap and interfere with one another.

Interference can be constructive or destructive:
  • Constructive interference: When waves align such that their peaks and troughs match, they add together, resulting in bright bands.
  • Destructive interference: When waves are out of phase and their peaks and troughs do not align, they cancel each other out, resulting in dark bands.
In Young's experiment, this pattern is observed on a screen and appears as alternating dark and bright fringes. The presence of an interference pattern indicates that the light is behaving like a wave, rather than just a particle. It's key for visualizing wave behavior in everyday physics applications.
Coherent Light
Coherent light means that the light waves maintain a constant phase relationship. This is essential for producing clear and stable interference patterns. When thinking about coherence, picture synchronized dancers who move in step perfectly.

In physics, coherence ensures that:
  • Light waves have the same frequency.
  • Light waves have a stable relative phase over time.
In Young’s double slit experiment, coherence is necessary for the distinct interference patterns to form. Without coherence, light waves won't align correctly, preventing constructive or destructive interference from occurring consistently. This is why in the exercise where different wavelengths (red and blue light) pass through the slits, no clear interference pattern arises. Each has a different wavelength, thus they lack the necessary coherence.
Light Wavelength
Wavelength is the distance between successive peaks of a wave. In terms of light, different colors correspond to different wavelengths, with red light having a longer wavelength than blue light.

Wavelength directly affects interference in several ways:
  • It determines the spacing between the bright and dark bands in the interference pattern.
  • Light of different wavelengths (like red and blue) results in patterns that do not overlap or match consistently unless other parameters are adjusted to create coherence.
In Young's double slit experiment, the filters cause each slit to emit light of a specific wavelength. When light of uniform wavelength passes through both slits, it’s easier for interference patterns to form because each wave maintains a consistent path difference. But if two different wavelengths are used simultaneously, the combination results in mixed but incoherent signals, which are not suitable for forming a standard interference pattern.

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Most popular questions from this chapter

In a biprism experiment, by using light of wavelength \(5000 \AA, 5 \mathrm{~mm}\) wide fringes are obtained on a screen \(1.0 \mathrm{~m}\) away from the coherent sources. The separation between the two coherent sources is (a) \(1.0 \mathrm{~mm}\) (b) \(0.1 \mathrm{~mm}\) (c) \(0.05 \mathrm{~mm}\) (d) \(0.01 \mathrm{~mm}\)

Air has refractive index \(1.003 .\) The thickness of air column, which will have one more wavelength of yellow light \((6000 \AA)\) than in the same thickness of vacuum is (a) \(2 \mathrm{~mm}\) (b) \(2 \mathrm{~cm}\) (c) \(2 \mathrm{~m}\) (d) \(2 \mathrm{~km}\)

In Young's double slit experiment, the two slits act as coherent sources of equal amplitude \(A\) and wavelength \(\lambda\). In another experiment with the same setup, the two slits are sources of equal amplitude \(A\) and wavelength \(\lambda\) but are incoherent. The ratio of the intensity of light at the mid- point of the screen in the first case to that in the second case is (a) \(2: 1\) (b) \(1: 2\) (c) \(3: 4\) (d) \(4: 3\)

In Young's double slit experiment, if \(d, D\) and \(\lambda\) represent, the distance between the slits, the distance of the screen from the slits and wavelength of light used respectively, then the bandwidth is inversely proportional to (a) \(\underline{\lambda}\) (b) \(d\) (c) \(D\) (d) \(\lambda^{2}\) (e) \(D^{2}\)

In Young's double slit experiment, the intensity on screen at a point where path difference is \(\lambda\) is \(K\). What will be intensity at the point where path difference is \(\lambda 4\) ? (a) \(\mathrm{K} / 4\) (b) \(K / 2\) (c) \(\bar{K}\) (d) zero

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