One day, after pulling down your window shade, you notice that sunlight is passing through a pinhole in the shade and making a small patch o

Question

One day, after pulling down your window shade, you notice that sunlight is passing through a pinhole in the shade and making a small patch of light on the far wall. Having recently studied optics in your physics class, you’re not too surprised to see that the patch of light seems to be a circular diffraction pattern. It appears that the central maximum is about 1 cm across, and you estimate that the distance from the window shade to the wall is about 4 m.

Estimate:
a. The average wavelength of the sunlight (in nm)
b. The diameter of the pinhole (in mm).

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RI SƠ 3 years 2021-08-10T09:28:16+00:00 1 Answers 172 views 0

Answers ( )

  1. phucdien
    0
    2021-08-10T09:29:22+00:00
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    Given that,

    Central maximum = 1 cm

    Distance from the window shade to the wall =4 m

    We know that,

    The visible range of the sun light is 400 nm to 700 nm.

    (a). We need to calculate the average wavelength

    Using formula of average wavelength

    \lambda_{avg}=\dfrac{\lambda_{1}+\lambda_{2}}{2}

    Put the value into the formula

    \lambda_{avg}=\dfrac{400+700}{2}

    \lambda_{avg}=550\ nm

    (b). We need to calculate the diameter of the pinhole

    Using formula for diameter

    w=\dfrac{2.44\lambda L}{D}

    D=\dfrac{2.44\lambda L}{w}

    Put the value into the formula

    D=\dfrac{2.44\times550\times10^{-9}\times4}{1\times10^{-2}}

    D=0.537\ mm

    Hence, (a). The average wavelength 550 nm.

    (b). The diameter of the pinhole is 0.537 mm.

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