Light from a helium-neon laser (λ=632.8 nm) passes through a pair of slits and forms an interfe

step 1 Hello and welcome to this video solution of numerate. So here is given that light from a helium

Light from a helium-neon laser (λ=632.8 nm) passes through...

Light from a helium-neon laser $(\lambda=632.8 \mathrm{~nm})$ passes through a pair of slits and forms an interference pattern on a screen located $1.40 \mathrm{~m}$ from the slits. Figure $18.37$ shows the interference pattern observed on the screen. What is the slit separation?

Key Concepts

Double-slit Interference

This concept explains how coherent light passing through two closely spaced slits produces a pattern of bright and dark fringes on a screen due to the superposition of waves emanating from each slit. The interference pattern is a classic demonstration of the wave nature of light.

Constructive Interference

Constructive interference occurs when the light waves from the two slits meet in phase, leading to bright fringes. It is governed by the condition that the path difference between the waves is an integer multiple of the wavelength, typically expressed as d sin? = m?, where m is an integer.

Small Angle Approximation

When the screen is far from the slits, the angles involved in the interference pattern are very small. Under such conditions, trigonometric functions can be approximated (sin? ? tan? ? y/L), simplifying the calculation of fringe positions and related quantities like slit separation.

Fringe Spacing

Fringe spacing is the distance between consecutive bright or dark fringes in the interference pattern. It is related to the wavelength of the light, the distance from the slits to the screen, and the slit separation (given by ?y = ?L/d). This relationship is key in determining unknown parameters such as the slit separation.

Transcript

00:01 Hello and welcome to this video solution of numerate.

00:04 So here is given that light from a helium neon laser having wavelength lambda equal to 632 .8 nanometers passes through a pair of slits and forms interference pattern as shown in this screen located as at a distance of let's say capital d which is 1 .4 meters from this slit.

00:29 The figure 18 .37 shows the interference pattern observed on the screen.

00:34 So it's sort of like this.

00:40 And here we have got this distance is given as 23 millimeters.

00:49 So that means the distance in 4 successive intensity maximum happens on the screen.

01:02 This 4, so this is a let's say this is 23 millimeters which is 23 times 10 to the power of minus 3 meters.

01:12 Right.

01:13 Let's say now the distance between two consecutive maxima.

01:20 Let me write this distance between two consecutive maxima will be this l by 4 which is let's say y that is equal to l by 4.

01:41 Right.

01:42 And this is equal to at least 23 times 10 to the power of minus 3 if you divide by 4 it will be 5 .75 times 10 to the power of minus 3 meters.

01:56 Right.

02:00 Now you can simply apply the conditions for maximum intensity that is d sine theta will be equal to m lambda.

02:13 Right.

02:16 This is the condition for maxima.

02:23 Right.

02:26 Right.

02:26 Or in other words you will have tan theta that is equal to y by d.

02:37 Right.

02:38 So let me just draw a simple diagram.

02:41 So let's say you have got this slit.

02:44 Right...

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