How many slits per centimeter must a grating have if there is to be no second-order spectrum for any visible wavelength?

Monochromatic light falls on a transmission diffraction grating at an angle Φ to the normal.

(a) Show that Eq. 35–13 for diffraction maxima must be replaced by d(sinΦ + sinθ) = ±mλ. m = 0, 1, 2, ...

(b) Explain the ± sign.

(c) Green light with a wavelength of 550 nm is incident at an angle of 15° to the normal on a diffraction grating with 4500 slits/cm. Find the angles at which the first-order maxima occur.

A diffraction grating has 15,000 rulings in its 1.9 cm width. Determine (a) its resolving power in first and second orders, and (b) the minimum wavelength resolution (∆λ) it can yield for λ = 410 nm.

When yellow sodium light, λ = 589nm, falls on a diffraction grating, its first-order peak on a screen 62.0 cm away falls 3.32 cm from the central peak. Another source produces a line 3.71 cm from the central peak. What is its wavelength? How many slits/cm are on the grating?

A He–Ne gas laser which produces monochromatic light of wavelength λ = 6.328 x 10^-7 m is used to calibrate a reflection grating in a spectroscope. The first-order diffraction line is found at an angle of 18.5° to the incident beam. How many lines per meter are imprinted on this reflecting diffraction grating?

If X-ray diffraction peaks corresponding to the first three orders ( m = 1, 2, and 3) are measured, can both the X-ray wavelength λ and lattice spacing d be determined? Prove your answer.

(a) Derive an expression for the intensity in the interference pattern for three equally spaced slits. Express in terms of δ = 2πd sin θ / λ where d is the distance between adjacent slits and assume the slit width D ≈ λ.

(b) Show that there is only one secondary maximum between principal peaks.

Suppose the angles measured in Problem 42 were produced when the spectrometer (but not the source) was submerged in water. What then would be the wavelengths (in air)?

Red laser light from a He–Ne laser (λ = 632.8 nm) creates a second-order fringe at 53.2° after passing through a grating. What is the wavelength λ of light that creates a first-order fringe at 21.2°?