If a diffraction grating produces a first-order (i) maximum...

If a diffraction grating produces a first-order (i) maximum for the shortest wavelength of visible light at $30.0^{\circ},$ at what angle will the first-order maximum be for the largest wavelength of visible light?

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Key Concepts

Diffraction Grating Equation

This is the fundamental relationship for a diffraction grating, given by d sin(?) = m?, where d is the spacing between the grating lines, ? is the diffraction angle, m is the order of the maximum, and ? is the wavelength of the light. It describes how light of different wavelengths is diffracted into different angles when passing through a grating.

Order of Maximum

The order of maximum refers to the sequence (m = 0, 1, 2, ...) of bright fringes produced by the interference of light diffracted from the grating. Each order corresponds to an integer multiple of the wavelength and determines the angular positions of these maxima according to the diffraction grating equation.

Wavelength Dependence in Diffraction

The angle at which a maximum occurs is directly proportional to the wavelength of the incident light for a fixed order. This means that as the wavelength increases, the diffraction angle also increases, leading to the dispersion of light into its constituent colors in a diffraction pattern.

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