1. A beam of 580-nm light passes through two
closely spaced glass plates, as shown in the figure.
For what minimum nonzero value of the plate
separation d is the transmitted light bright?
Ans. 290 nm
2. A piece of transparent material having an index of
refraction n is cut into the shape of a wedge as
shown in the figure. The angle of the wedge is
small. Monochromatic light of wavelength λ is
normally incident from above, and viewed from
above. Let h represent the height of the wedge and
ℓ its width. Show that bright fringes occur at the positions x = λℓ(m +
½)/2hn and dark fringes occur at the positions x = λℓm/2hn, where m = 0, 1,
2, . . . and x is measured as shown.
3. Consider the double-slit arrangement
shown in the figure, where the slit
separation is d and the slit to screen
distance is L. A sheet of transparent plastic
having an index of refraction n and
thickness t is placed over the upper slit. As
a result, the central maximum of the
interference pattern moves upward a
distance y’. Find y’.
Ans.
(n  1) Lt
d  (n  1) 2 t 2
2
4. A thin flake of mica (n = 1.58) is used to cover one slit of a double-slit
interference arrangement. The central point on the viewing screen is now occupied
by what had been the seventh bright side fringe (m = 7). If  = 550 nm, what is the
thickness of the mica?
Ans. 6.64×10-6 m
5. In the figure, a broad beam of light of wavelength 630
nm is sent directly downward through the top plate of a
pair of glass plates touching at the left end. The air
between the plates acts as a thin film, and an
interference pattern can be seen from above the plates.
Initially, a dark fringe lies at the left end, a bright fringe
lies at the right end, and nine dark fringes lie between
those two end fringes. The plates are then very gradually squeezed together at a
constant rate to decrease the angle between them. As a result, the fringe at the
right side changes between being bright to being dark every 15.0 s (a) At what rate
is the spacing between the plates at the right end being changed? (b) By how
much has the spacing there changed when both left and right ends have a dark
fringe and there are five dark fringes between them?
Ans. (a) 10.3 nm/s (b) 1.10 m
6. Figure (a) shows a lens with radius of curvature R lying on a flat glass plate and
illuminated from above by light with wavelength . Figure (b) (a photograph
taken from above the lens) shows that circular interference fringes (called
Newton’s rings) appear, associated with the variable thickness d of the air film
between the lens and the plate. Find the radii r of the interference maxima
assuming r/R << 1.
Ans.
1
(m  ) R , m = 0, 1, 2, …
2
7. A thin film with index of refraction n = 1.44 is placed in one arm of a Michelson
interferometer, perpendicular to the optical path. If this causes a shift of 7.0 bright
fringes of the pattern produced by light of wavelength 589 nm, what is the film
thickness?
Ans. 4.7 m
8. In the figure, an airtight chamber of length d = 5.0 cm
is placed in one of the arms of a Michelson
interferometer. (The glass window on each end of the
chamber has negligible thickness.) Light of wavelength
 = 500 nm is used. Evacuating the air from the
chamber causes a shift of 60 bright fringes. From these
data and to six significant figures, find the index of
refraction of air at atmospheric pressure.
Ans. 1.00030