What are the steps to determine the spacing between slits in a diffraction grating and the angle to the third-order maximum when light from a 633-nm laser beam is incident on it with 3.79 x 105 lines/m?
The spacing between slits in the grating is 2.64 x 10^-6 m. The angle to the third-order maximum is 0.0415 radians or approximately 2.38 degrees.
Understanding Diffraction Grating
Diffraction grating is a device used in optics to separate polychromatic light into its different colors. It consists of a large number of evenly spaced parallel slits or lines that diffract the light passing through them. When light encounters a diffraction grating, it produces interference patterns due to the wave nature of light.
Calculating the Spacing Between Slits
To determine the spacing (d) between slits in the grating, we use the formula d = 1/(number of lines per meter). In this case, the number of lines per meter is given as 3.79 x 10^5. Therefore, d = 1/(3.79 x 10^5) = 2.64 x 10^-6 m. This is the spacing between the slits in the diffraction grating.
Calculating the Angle to the Third-Order Maximum
The angle to the third-order maximum can be calculated using the grating equation: d*sin(theta) = m*lambda, where d is the spacing between slits, theta is the angle to the maximum, m is the order of the maximum, and lambda is the wavelength of the light. By rearranging the equation, we get theta = arcsin(m*lambda/d).
Substituting the given values - m = 3 (third-order maximum), lambda = 633 x 10^-9 m (633-nm laser beam), and d = 2.64 x 10^-6 m, we get theta = arcsin(3*633 x 10^-9/2.64 x 10^-6) = 0.0415 radians or approximately 2.38 degrees.
Understanding these calculations helps in interpreting the behavior of light when passing through a diffraction grating and how the spacing and angles play a crucial role in the resulting interference pattern.