# 3.1 Young's double-slit interference  (Page 2/5)

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Young used sunlight, where each wavelength forms its own pattern, making the effect more difficult to see. In the following discussion, we illustrate the double-slit experiment with monochromatic    light (single $\lambda$ ) to clarify the effect. [link] shows the pure constructive and destructive interference of two waves having the same wavelength and amplitude. The amplitudes of waves add. (a) Pure constructive interference is obtained when identical waves are in phase. (b) Pure destructive interference occurs when identical waves are exactly out of phase, or shifted by half a wavelength.

When light passes through narrow slits, the slits act as sources of coherent waves and light spreads out as semicircular waves, as shown in [link] (a). Pure constructive interference occurs where the waves are crest to crest or trough to trough. Pure destructive interference occurs where they are crest to trough. The light must fall on a screen and be scattered into our eyes for us to see the pattern. An analogous pattern for water waves is shown in [link] . Note that regions of constructive and destructive interference move out from the slits at well-defined angles to the original beam. These angles depend on wavelength and the distance between the slits, as we shall see below. Double slits produce two coherent sources of waves that interfere. (a) Light spreads out (diffracts) from each slit, because the slits are narrow. These waves overlap and interfere constructively (bright lines) and destructively (dark regions). We can only see this if the light falls onto a screen and is scattered into our eyes. (b) When light that has passed through double slits falls on a screen, we see a pattern such as this.

To understand the double-slit interference pattern, consider how two waves travel from the slits to the screen ( [link] ). Each slit is a different distance from a given point on the screen. Thus, different numbers of wavelengths fit into each path. Waves start out from the slits in phase (crest to crest), but they may end up out of phase (crest to trough) at the screen if the paths differ in length by half a wavelength, interfering destructively. If the paths differ by a whole wavelength, then the waves arrive in phase (crest to crest) at the screen, interfering constructively. More generally, if the path length difference $\text{Δ}l$ between the two waves is any half-integral number of wavelengths [(1 / 2) $\lambda$ , (3 / 2) $\lambda$ , (5 / 2) $\lambda$ , etc.], then destructive interference occurs. Similarly, if the path length difference is any integral number of wavelengths ( $\lambda$ , 2 $\lambda$ , 3 $\lambda$ , etc.), then constructive interference occurs. These conditions can be expressed as equations:

$\text{Δ}l=m\lambda ,\phantom{\rule{0.8em}{0ex}}\text{for}\phantom{\rule{0.2em}{0ex}}m=0,\text{±}1,\text{±}2,\text{±}3\phantom{\rule{0.2em}{0ex}}\dots \phantom{\rule{0.2em}{0ex}}\text{(constructive interference)}$
$\text{Δ}l=\left(m+\frac{1}{2}\right)\lambda ,\phantom{\rule{0.8em}{0ex}}\text{for}\phantom{\rule{0.2em}{0ex}}m=0,\text{±}1,\text{±}2,\text{±}3\phantom{\rule{0.2em}{0ex}}\dots \phantom{\rule{0.2em}{0ex}}\text{(destructive interference)}$ Waves follow different paths from the slits to a common point P on a screen. Destructive interference occurs where one path is a half wavelength longer than the other—the waves start in phase but arrive out of phase. Constructive interference occurs where one path is a whole wavelength longer than the other—the waves start out and arrive in phase.

## Summary

• Young’s double-slit experiment gave definitive proof of the wave character of light.
• An interference pattern is obtained by the superposition of light from two slits.

## Conceptual questions

Young’s double-slit experiment breaks a single light beam into two sources. Would the same pattern be obtained for two independent sources of light, such as the headlights of a distant car? Explain.

No. Two independent light sources do not have coherent phase.

Is it possible to create a experimental setup in which there is only destructive interference? Explain.

Why won’t two small sodium lamps, held close together, produce an interference pattern on a distant screen? What if the sodium lamps were replaced by two laser pointers held close together?

Because both the sodium lamps are not coherent pairs of light sources. Two lasers operating independently are also not coherent so no interference pattern results.

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a thermodynamic quantity equivalent to the total heat content of a system
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proparty of tharmo dainamic
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kenneth
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There are three sets of three neutrons, 9.
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A positron is composed of the first three dimensions.
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An electron is composed of the second three dimensions.
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I hope I'm clear if I'm not please tell me to clarify further or rephrase
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Swagatika
3×10^8
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কাজের একক কী
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Energy is ability so capacity to do work.
kenneth
friction ka direction Kaise pata karte hai
friction is always in the opposite of the direction of moving object
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