27.4 Multiple Slit Diffraction

Which of the following cannot be a possible outcome of passing white light through several evenly spaced parallel slits?

1. The central maximum will be white but the higher-order maxima will disperse into a rainbow of colors.
2. The central maximum and higher-order maxima will be of equal widths.
3. The lower wavelength components of light will have less diffraction compared to higher wavelength components…

A diffraction grating has 2000 lines per centimeter. At what angle will the first-order maximum be for 520-nm-wavelength green light?

How many lines per centimeter are there on a diffraction grating that gives a first-order maximum for 470-nm blue light at an angle of $\text{25} . 0º$?

Calculate the wavelength of light that has its second-order maximum at $\text{45} . 0º$ when falling on a diffraction grating that has 5000 lines per centimeter.

(a) What do the four angles in the above problem become if a 5000-line-per-centimeter diffraction grating is used? (b) Using this grating, what would the angles be for the second-order maxima? (c) Discuss the relationship between integral reductions in lines per centimeter and the new angles of various order maxima.

The yellow light from a sodium vapor lamp seems to be of pure wavelength, but it produces two first-order maxima at $\text{36} . \text{093} º$ and $\text{36} . \text{129} º$ when projected on a 10,000 line per centimeter diffraction grating. What are the two wavelengths to an accuracy of 0.1 nm?

Structures on a bird feather act like a reflection grating having 8000 lines per centimeter. What is the angle of the first-order maximum for 600-nm light?

At what angle does a diffraction grating produces a second-order maximum for light having a first-order maximum at $\text{20} . 0º$?

If a diffraction grating produces a first-order maximum for the shortest wavelength of visible light at $\text{30} . 0º$, at what angle will the first-order maximum be for the longest wavelength of visible light?

(a) Show that a 30,000-line-per-centimeter grating will not produce a maximum for visible light. (b) What is the longest wavelength for which it does produce a first-order maximum? (c) What is the greatest number of lines per centimeter a diffraction grating can have and produce a complete second-order spectrum for visible light?

(a) What visible wavelength has its fourth-order maximum at an angle of $\text{25}.\text{0}º$ when projected on a 25,000-line-per-centimeter diffraction grating? (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?