Light of wavelength 500 nm is incident normally on a diffraction grating. If the third-order max

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Light of wavelength 500 nm is incident normally on a...

Light of wavelength $500 \mathrm{nm}$ is incident normally on a diffraction grating. If the third-order maximum of the diffraction pattern is observed at $32.0^{\circ},$ (a) what is the number of rulings per centimeter for the grating? (b) Determine the total number of primary maxima that can be observed in this situation.

Key Concepts

Diffraction Grating Equation

The diffraction grating equation, given by d*sin(?) = m*?, is central to understanding how light interferes to produce maxima or orders in a diffraction pattern. In this equation, d represents the distance between adjacent slits on the grating, ? is the angle measured from the normal to the grating at which a maximum occurs, m is the order of the maximum (an integer), and ? is the wavelength of the incident light. This equation allows one to predict the angles at which bright fringes will be observed when coherent light is diffracted by a grating.

Grating Ruling Density

Grating ruling density refers to the number of slits (or rulings) per unit length on a diffraction grating. It is directly related to the grating spacing (d), the distance between adjacent slits, by the relation d = 1/N, where N is the number of lines per unit length. A higher ruling density implies a smaller slit spacing, which in turn affects the angular spread of the diffraction orders and the resolution of the grating in separating different wavelengths.

Maximum Order of Diffraction

The maximum order of diffraction that can be observed is determined by the physical constraint that the sine of the diffraction angle cannot exceed 1. This leads to the requirement that m*?/d must be less than or equal to 1, thereby limiting the integer values of m that result in a real angle. This concept is essential in understanding the full diffraction pattern, as it defines the range of observable primary maxima in a grating experiment.

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