Light emitted by element X passes through a diffraction grating that has 1200 slits/mm. The interference pattern is observed on a screen 77.

Question

Light emitted by element X passes through a diffraction grating that has 1200 slits/mm. The interference pattern is observed on a screen 77.0 cm behind the grating. First-order maxima are observed at distances of 58.0 cm , 65.4 cm , and 94.5 cm from the central maximum. What are the wavelengths of light emitted by element X?

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RuslanHeatt 4 years 2021-08-13T07:13:06+00:00 1 Answers 33 views 0

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  1. Orla
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    2021-08-13T07:14:30+00:00
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    Answer:

    500 nm, 530 nm, 650 nm

    Explanation:

    Let’s say that there is diffraction grating observed with a slit spacing of s. Respectively we must determine the angle θ which will help us determine the 3 wavelengths ( λ ) of the light emitted by element X. This can be done applying the following formulas,

    s( sin θ ) = m * λ, such that y = L( tan θ ) – where y = positioning, or the distance of the first – order maxima, and L = constant, of 77 cm

    Now the grating has a slit spacing of –

    s = 1 / N = 1 / 1200 = 0.833 * 10⁻³ mm

    The diffraction angles of the ” positionings ” should thus be –

    θ = tan⁻¹ * ( 0.58 / 0.77 ) = 37°,

    θ = tan⁻¹ * ( 0.654 / 0.77 ) = 40°,

    θ = tan⁻¹ * ( 0.945 / 0.77 ) = 51°

    The wavelengths of these three bright fringes should thus be calculated through the formula : λ = s( sin θ ) –

    λ = 0.833 * 10⁻³ * sin( 37° ) = ( 500 * 10⁻⁹ m )

    λ = 0.833 * 10⁻³ * sin( 40° ) = ( 530 * 10⁻⁹ m )

    λ = 0.833 * 10⁻³ * sin( 51° ) = ( 650 * 10⁻⁹ m )

    Wavelengths : 500 nm, 530 nm, 650 nm

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