Laser light is passed through a diffraction grating with...

Laser light is passed through a diffraction grating with 7000 lines per centimeter. Light is projected onto a screen far away. An observer by the diffraction grating observes the first order maximum $25^{\circ}$ away from the central maximum. (a) What is the wavelength of the laser? (b) If the first order maximum is $40 \mathrm{~cm}$ away from the central maximum on the screen, how far away is the screen from the diffraction grating? (c) How far, measured along the screen, from the central maximum will the second-order maximum be?

Laser light is passed through a diffraction grating with 7000 lines per centimeter. Light is projected onto a screen far away. An observer by the diffraction grating observes the first order maximum $25^{\circ}$ away from the central maximum.
(a) What is the wavelength of the laser?
(b) If the first order maximum is $40 \mathrm{~cm}$ away from the central maximum on the screen, how far away is the screen from the diffraction grating?
(c) How far, measured along the screen, from the central maximum will the second-order maximum be?

Key Concepts

Diffraction Grating

A diffraction grating is an optical component with a periodic structure that splits and diffracts light into several beams traveling in different directions. The directions of these diffracted beams depend on the spacing of the grating and the wavelength of the light, leading to a pattern of maxima and minima caused by constructive and destructive interference.

Grating Equation

The grating equation, given by d sin ? = m?, relates the spacing between the grating lines (d), the diffraction angle (?), the order of the maximum (m), and the wavelength of the light (?). This equation is fundamental for determining any one of these quantities when the others are known, and is used widely in spectroscopy and optical physics.

Diffraction Order

Diffraction orders (denoted by m) refer to the different sets of maxima that appear at specific angles. The order number indicates how many wavelengths of path difference have been introduced between adjacent slits. The central maximum is the zero order (m = 0), while higher orders (m = 1, 2, etc.) occur at increasing angles as determined by the grating equation.

Screen Geometry

In diffraction experiments, screen geometry connects the observed displacement of diffraction maxima on a screen to the physical distance between the grating and the screen. Using trigonometric relationships, such as tan ?, one can determine the distance from the grating to the screen based on the observed positions of the diffraction orders, linking angular measurements with linear distances.

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