Chapter 33, Problem 74EAP

FIGURE CP33.74 shows light of wavelength ? incident at angle on $\varphi$ a reflection grating of spacing d. We want to find the angles ${\theta }_m$ at which constructive interference occurs.

a. The figure shows paths 1 and 2 along which two waves travel and interfere. Find an expression for the path-length difference $\Delta r=r_2-r_1$ .

b. Using your result from part a, find an equation (analogous to Equation 33.15) for the angles ${\theta }_m$ at which diffraction occurs when the light is incident at angle $\varphi$ . Notice that m can be a negative integer in your expression, indicating that path 2 is shorter than path 1.

c. Show that the zeroth-order diffraction is simply a “reflection.” That is, ${\theta }_m=\varphi$ .

d. Light of wavelength 500 nm is incident at $\varphi =40°$ on a reflection grating having 700 reflection lines/mm. Find all angles ${\theta }_m$ at which light is diffracted. Negative values of ${\theta }_m$ are interpreted as an angle left of the vertical.

e. Draw a picture showing a single 500 nm light ray incident at $\varphi =40°$ and showing all the diffracted waves at the correct angles.

FIGURE CP33.74