What is the highest spectral order that can be seen if a grating with 6800 slits per cm is illuminated with 633-nm laser light? Assume normal incidence.

검증된 단계별 안내

Calculate the slit spacing (d) by taking the reciprocal of the number of slits per unit length. Since there are 6800 slits per cm, convert this to meters for standard SI units.

Use the grating equation for normal incidence, which is given by \(m \lambda = d \sin \theta\). Here, \(m\) is the order of the spectrum, \(\lambda\) is the wavelength of the light, and \(\theta\) is the angle of diffraction. For normal incidence, \(\theta\) is the angle relative to the normal of the grating.

Since the maximum angle \(\theta\) can be is 90 degrees (beyond which no light is diffracted), set \(\sin \theta = 1\) in the grating equation to find the maximum possible order \(m\).

Substitute the values of \(\lambda\) (633 nm converted to meters) and \(d\) into the modified grating equation \(m \lambda = d\) to solve for \(m\).

The highest possible order, \(m\), is the largest integer value that satisfies the equation without exceeding the value calculated in the previous step.

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주요 개념

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Diffraction Grating

A diffraction grating is an optical component with a periodic structure that disperses light into its component wavelengths. The number of slits per unit length determines the grating's resolving power and the angles at which different wavelengths are diffracted. In this case, the grating has 6800 slits per cm, which affects the maximum order of diffraction that can be observed.

Order of Diffraction

The order of diffraction refers to the integer multiples of the wavelength that can be observed in the diffraction pattern produced by a grating. The first order (m=1) corresponds to the angle where the first maximum occurs, and higher orders (m=2, m=3, etc.) correspond to subsequent maxima. The maximum observable order is limited by the grating equation and the wavelength of the light used.

Grating Equation

The grating equation, given by d sin(θ) = mλ, relates the angle of diffraction (θ), the wavelength of light (λ), the grating spacing (d), and the order of diffraction (m). Here, d is the distance between adjacent slits, which can be calculated from the number of slits per cm. This equation is essential for determining the maximum order of diffraction that can be achieved with a given wavelength and grating.

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교과서 질문

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