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Coherent light of frequency 6.32×1014 Hz passes through two thin slits and falls on a screen 87.0 cm away. You observe that the third bright fringe occurs at 3.16 cm on either side of the central bright fringe.

At what distance from the central bright fringe will the third dark fringe occur?

Respuesta :

Answer:

[tex]y_{osc}[/tex]= 4,574 10⁻⁵ m

Explanation:

The interference pattern for a two slit system is given by

    d sin θ = m λ                 constructive interference

    d sin θ= (m + ½) λ          destructive interference

In general and also in this case the screen is far from the slits, so the TT-free can approach the TT

    tan θ = y / L

Let's replace

     d y / L = m λ                   constructive interference

     d y / L = (m + ½) λ          destructive interference

Let's start when there is constructive interference

They give us the frequency of light, let's find the wavelength

    c = λ f

    λ = c / f

    λ = 3 10⁸ / 6.32 10¹⁴

    λ = 4.7468 10⁻⁷ m

Let's take the opportunity to reduce the SI system

    L = 87 cm = 0.87 m

    y = 3.16 cm = 0.0316 m

Now we can find the separation of the slits

   d = m λ L / Y

   d = 3 4.7468 10⁻⁷ 0.87 / 0.0316

   d = 3.92 10⁻⁵ m

We already have all the data, now let's use the destructive interference equation and find [tex]y_{osc}[/tex]

   d [tex]y_{osc}[/tex] / L = (m + ½) λ

   [tex]y_{osc}[/tex] = (m + ½) λ L / d

  [tex]y_{osc}[/tex] = (3 + ½) 4.7468 10⁻⁷ 0.87 / 0.0316

 [tex]y_{osc}[/tex]= 4,574 10⁻⁵ m

Lanuel

The distance from the central bright fringe at which the third dark fringe would occur is equal to 2.63 cm.

Given the following data:

  • Frequency = 6.32 × 10¹⁴
  • Length, L = 87.0 cm to m = 0.87 m.
  • Bright fringe, y = 3.16 cm to m = 0.0316 m.
  • Order of fringe, m = 3.

How to calculate the distance?

Mathematically, the interference pattern for a two-slit system is given by these formulas:

dsinθ = mλ      ..................constructive interference.

dsinθ = (m + ½)λ    ............d. interference.

Note: Speed of light is equal to 3 × 10⁸ m/s.

We need to determine the wavelength of this coherent light as follows:

λ = c/f

λ = 3 × 10⁸/6.32 × 10¹⁴

λ = 4.75 × 10⁻⁷ m

λ = 4.75 nm.

Next, we would determine the separation (distance) between the slits:

d = mλL/y

d = (3 × 4.75 × 10⁻⁷ × 0.87)/0.0316

d = 3.92 × 10⁻⁵ m.

Now, we can determine the distance from the central bright fringe:

θ = (m + ½)λ/d

θ = [(2 + ½) × 4.75 × 10⁻⁷]/3.92 × 10⁻⁵

θ = 0.0303 rad.

y = Lθ

y = 0.87 × 0.0303

y = 0.0263 m to cm;

y = 2.63 cm.

Read more on wavelength here: brainly.com/question/14702686

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