A grating has exactly 8000 slits uniformly spaced over 2.54 cm and is illuminated by light from

A grating has exactly 8000 slits uniformly spaced over 2.54...

A grating has exactly 8000 slits uniformly spaced over $2.54 \mathrm{~cm}$ and is illuminated by light from a mercury vapor discharge lamp. What is the expected angle for the third-order maximum of the green line $(\lambda=546 \mathrm{~nm}) ?$

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Key Concepts

Calculation of Slit Spacing

When a grating has a given number of slits over a determined distance, the slit spacing (d) is calculated by dividing the total length by the number of slits. This spacing is a critical parameter in the grating equation for determining diffraction angles.

Diffraction Grating

A diffraction grating is an optical device with many equally spaced slits that separates light into its component wavelengths. The specific pattern of light—constructive and destructive interference—produced when the light waves overlap, is used to analyze the light’s spectral properties.

Grating Equation

The grating equation, d sin ? = m?, relates the light's wavelength, the spacing of the slits, and the order of the maximum (m) to the observable diffraction angle (?). This equation is fundamental in predicting where bright fringes appear in a diffraction pattern.

Diffraction Order

Diffraction order (m) refers to the integer multiples in the grating equation and corresponds to the various observed maxima in the diffraction pattern. Higher values of m indicate higher order maxima at larger angles, provided that the sine function remains within its valid range.

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