Diffraction and Interference (Light)

Problems

practice

1. Measuring the thickness of human hair.
2. Write something else.
3. Write something different.
4. Write something completely different.

conceptual

1. Suppose you were the owner of a radio station and that you wanted to extend the range of your broadcast. Would it be wise to erect a second transmitting antenna to broadcast simultaneously with the first? How will a second transmitter affect reception? Explain your reasoning.
2. For what portion of the electromagnetic spectrum could a picket fence be used as a diffraction grating? Explain your reasoning.
3. For each of the following examples, state whether the source of light produces a spectrum that is mostly continuous or mostly discrete. Compile your results in a table like the one below.

   Identify the spectral type with a check mark (√)

   source	continuous	discrete
   blow torch
   candle flame
   cathode ray tube
   emission nebula
   firefly
   fluorescent tube
   glow stick
   incandescent bulb
   laser
   LED
   neon sign
   plasma display
   the Sun
   red hot metal

numerical

1. The prominent yellow color of excited sodium vapor comes from two lines with nearly the same wavelength — the D lines at 589.0 nm and 589.6 nm. A diffraction grating with 531.5 lines per mm is to be used to observe the discrete spectrum of sodium.
   1. Determine the angular separation between the D lines.
   2. How far away would an observing screen have to be placed for the D lines to be separated by 1.0 mm?
2. A diffraction grating has 5360 lines per cm.
   1. What range of angles do the visible wavelengths (400–700 nm) span in first order maxima?
   2. How wide would a screen have to be to capture this range of wavelengths if it was placed 1.00 m away?

statistical

1. An unmarked diffraction grating was used to observe the spectrum of hydrogen. A screen was placed 1.0 m away and the distance from the central maximum to the first order bright fringe was measured for each of the four visible lines in the spectrum. The wavelengths of the lines were taken from the National Institute of Standards and Technology Atomic Spectra Database. The data were compiled in a table like the one below.

   The spectrum of hydrogen

   name	color	λ (nm)	x (mm)	λ (mm)	sin θ
   α	violet	410	452
   β	violet	434	483
   γ	blue	486	558
   δ	red	656	874

   1. Complete the table by converting the wavelength to millimeters and computing the sine of the angle of the fringe.
   2. Construct a graph using the data in the last two columns.
   3. Determine the line of best fit.
   4. Determine the number of lines per millimeter on the unmarked diffraction grating.