Although we have discussed single-slit diffraction only for...

Although we have discussed single-slit diffraction only for a slit, a similar result holds when light bends around a straight, thin object, such as a strand of hair. In that case, $a$ is the width of the strand. From actual laboratory measurements on a human hair, it was found that when a beam of light of wavelength $632.8 \mathrm{nm}$ was shone on a single strand of hair, and the diffracted light was viewed on a screen $1.25 \mathrm{~m}$ away, the first dark fringes on either side of the central bright spot were $5.22 \mathrm{~cm}$ apart. How thick was this strand of hair?

Transcript

00:01 Hi there, so for this problem we are told that although we have discussed single sleet diffraction only for a sleet, a similar result holds when light bends around a straight, thin object, such an strad of herd.

00:17 In that case, a is the width of the strat.

00:20 So, from actual laboratory measurements on a human herd, it was found that when a beam of light of a wavelength that is given, and that wavelength is equal to 632 .8 nanometers, nanometers, was shown on a single strut of herd, and the defrapted line was view on a screen, that it is at a distance of the word going to call capital l, that is equal to 1 .25 meters.

01:01 The first dark fringes on either side of the central bright spot were 5 .22 centimeters apart.

01:12 So we're going to call this the distance, yes, we're going to call this the distance y.

01:27 That is going to be a value in this case of 5 .22 centimeters.

01:41 So that is the same as 5 .22 times 10 to the minus 2 meters.

01:59 So for this disruption problem, they tell us that it is equivalent to the disruption.

02:12 Oh, sorry.

02:13 Well, the question is, how thick was this strut of herd? so we need to calculate the value of a.

02:22 Now, again, we know that for this problem, they tell us that it is equivalent to the disruption of a single slit, which is explained by the following equation.

02:31 That is that the thickness of the herd is equal to the function sign of theta, and then this is equal to plus or minus the order m times the wavelength.

02:50 Now, we can see that the disruption angle is missing in this case, but we can find it by trigonometry, where l is the distance of the strand of the herd to the observation screen, and y is the perpendicular distance to the first minimum intensity.

03:09 So remember that those values are given, l is equal to 1 .25 meters, and y is 5 .22 times 10 to the minus 2 meters, or 5 .22 centimeters.

03:19 Meters.

03:20 So we know that they are related by the tangent of theta by trigonometry.

03:25 That will be y divided by lt...

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