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23 January, 23:45

Two lasers are shining on a double slit, with slit separationd. Laser 1 has a wavelength of d/20, whereas laser 2 has a wavelength of d/15. The lasers produce separate interference patternson a screen a distance 5.00 {/rm m} away from the slits.

Part A

Which laser has its first maximum closer to the centralmaximum?

Part B

What is the distance Deltay_max-max between the first maxima (on the same side of thecentral maximum) of the two patterns?

Part B. 1

Find the location of the first maximum for laser1

Part B. 2

Find the location of the first maximum for laser2Part C

What is the distance Deltay_max-min between the second maximum of laser 1 and the thirdminimum of laser 2, on the same side of the central maximum?

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Answers (1)
  1. 24 January, 00:11
    0
    a) laser 1 has the maximum closest to the central maximum

    b) y₂ - y₁ = L 1.66 10⁻²

    Explanation:

    a), B1, B2) The expression that describes the constructive interference for a double slit is

    d sin θ = m λ

    The pattern is observed on a screen

    tan θ = y / L

    Since the angles are very small

    tan θ = sin θ / cos θ = sin θ = y/L

    d y / L = m λ

    In this case the laser has a wavelength

    λ ₁ = d/20

    We substitute

    d y / L = m d / 20

    m = 1

    y₁ = L / 20

    For the laser 2 λ ₂ = d / 15

    y₂ = L / 15

    When examining the two expressions, laser 1 has the maximum closest to the central maximum

    b) the difference between the two patterns is

    y₂ - y₁ = L (1/15 - 1/20)

    y₂ - y₁ = L 1.66 10⁻²

    C) laser 1 second maximum

    y₁ ' = 2 L / 20

    y₁ ' = L 0.1

    Laser 2 third minimum

    To have a minimum, the equation must be satisfied

    d sin θ = (m + ½) λ

    d y / L = (m + ½) λ

    d y / L = (m + ½) d / 15

    y = L (m + 1/2) / 15

    m = 3

    y₂' = L (3 + ½) / 15

    y₂' = L 0.2333

    The difference is

    y₁ ' - y₂' = L (0.1 - 0.2333)

    y₁ '-y₂' = L (-0.133)
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