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konstantin123 [22]
3 years ago
12

Although we have discussed single-slit diffraction only for a slit, a similar result holds when light bends around a straight, t

hin 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 633.0 nm was shone on a single strand of hair, and the diffracted light was viewed on a screen 1.25 m away, the first dark fringes on either side of the central bright spot were 5.06 cm apart. How thick was this strand of hair???
Physics
1 answer:
user100 [1]3 years ago
8 0

Answer:

The width of the strand of hair is   1.96 10⁻⁵ m

Explanation:

For this diffraction problem they tell us that it is equivalent to the diffraction of a single slit, which is explained by the equation

<h3>       a sin θ =±  m λ </h3><h3 />

Where the different temrs are: “a” the width of the hair, λ the wavelength, θ the angle from the center, m the order of diffraction, which is the number of bright rings (constructive diffraction)  

We can see that the diffraction angle is missing, but we can find it by trigonometry, where L is the distance of the strand of hair to the observation screen and "y" is the perpendicular distance to the first minimum of intensity

        L = 1.25 m 100 cm/1m   = 125 cm

       y = 5.06 cm  

      Tan θ = y/L

      Tan θ = 5.06/125

      θ = tan⁻¹ ( 0.0405)

      θ =  2.32º

With this data we can continue analyzing the problem, they indicate that they measure the distance to the first dark strip, thus m = 1

     a = m λ / sin θ

     a = 1 633 10⁻⁹ 1.25/sin 2.3

     a = 1.96 10⁻⁵ m  

     a = 0.0196 mm

The width of the strand of hair is   1.96 10⁻⁵ m

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The acceleration of gravity is always directed to the ground (down) and, near the surface of the earth, has a constant value of 9.8 m/s². Since the answer "b" is the only option with an acceleration of 9.8 m/s² directed downwards, that would solve the exercise. But why is the velocity zero at the highest point?

Let´s take a look at the height function:

h(t) = h0 + v0 · t + 1/2 g · t²

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v0 = initial velocity

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Notice that the function is a negative parabola if we consider downward as negative (in that case "g" would be negative). Then, the function has a maximum (the highest point) at the vertex of the parabola. At the maximum point, the slope of the tangent line to the function is zero, because the tangent line is horizontal at a maximum point. The slope of the tangent line to the function is the rate of change of height with respect to time, i.e, the velocity. Then, the velocity is zero at the maximum height.

Another way to see it (without calculus):

When the ball is going up, the velocity vector points up and the velocity is positive. After reaching the maximum height, the velocity vector points down and is negative (the ball starts to fall). At the maximum height, the velocity vector changed its direction from positive to negative, then at that point, the velocity vector has to be zero.

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<h3>What is work done?</h3>

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