# Exercise 4

```RÖ4
7-9: In an interference experiment of the Young type, the distance between slits is 0.5mm, ad the
wavelength of the light is 600 nm.
a. If it is desired to have a fringe spacing of 1 mm at the screen, what is the proper screen distance?
b. If a thin plate of glass (n=1.50) of thickness 100 microns is placed over one of the slits, what is the
lateral fringe displacement at the screen?
c. What path difference corresponds to a shift in the fringe pattern from a peak maximum to the (same)
peak half maximum?
7-14: Light of continuously variable wavelength illuminates normally a thin oil (index of 1.30) film on
a glass surface. Extinction of the reflected light is observed to occur at wavelengths of 525 and 675 nm
in the visible spectrum. Determine the thickness of the oil film and the orders of the interference.
8-3: A thin sheet of fluorite of index 1.434 is inserted normally into one beam of a Michelson
interferometer. Using light of wavelength 589 nm, the fringe pattern us found to shift by 35 fringes.
What is the thickness of the sheet?
11-15: A double-slit diffraction pattern is formed using mercury green light at 546.1 nm. Each slit has a
width 0.100 mm. The pattern reveals that the fourth-order interference maxima are missing from the
pattern.
a. What is the slit separation?
b. What is the irradiance of the first three orders of interference fringes, relative to the zeroth-order
maximum?
11-16:
a. Show that the number of bright fringes seen under the central diffraction peak in a Fraunhofer
double-slit pattern is given by 2(a/b) – 1, where a/b is the ratio of the slit separation.
b. How many fringes do you see for the case a/b=3/2 ?
c. If 13 bright fringes are seen in the central diffraction peak when the slit width is 0.30 mm, determine
the slit separation.
12-7 The two sodium D lines at 5893 Å are 6 Å apart. If a grating with only 400 grooves is available,
a. What is the lowest order possible in which the D lines are resolved?
b. How wide does the grating have to be?
Tentamen (2010-05-03, uppgift 5) : I figuren nedan ser vi ett enkelspalt diffraktions mönster och ett
dubbelspalt diffraktions mönster. Spaltöppningen är lika stor i båda fallen (=b). Avståndet mellan
spalterna är 0.7 mm.
a. Uppskatta storleken på spaltöppningen b genom att titta på dubbelspalts mönstret.
b. Om skärmen är 2 m bort från spalterna och det centrala mönstret från enkelspalts
diffraktion är 3 cm brett, vad är då våglängden av det infallande ljuset?
c. Vad är bredden av den centrala interferens linjen i dubbelspalt mönstret?
```
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