1. INTERFERENCE

2. 1. The double slit arrangement is illuminated by light of wavelength 546nm. The slits are 12mm apart and the screen on which interference pattern appears is 55cm away.
What is the angular position of (i) first minima and (ii) tenth maxima?
What is the separation between two adjacent maxima?

3. 2. Monochromatic light illuminates two parallel slits a distance d apart The first maximum is observed at an angular position of 15°. By what percentage should d be increased or decreased so that the second maximum will instead be observed at 15° ?
3. A double-slit arrangement produces interference fringes for sodium light (wavelength = 589 nm) that are 0.23° apart. For what wavelength would the angular separation be 10% greater ? Assume that the angle  is small.

4. 4. Two slits are 0. 08 mm apart, and the screen is 2 m away
4. Two slits are 0.08 mm apart, and the screen is 2 m away. How far is the third dark fringe located from the central maximum if λ = 600 nm?
Central maximum m=0
m=0
m=1
m=2
m=3

5. 5. In an interference experiment in a large ripple tank the coherent vibrating sources are placed 120 mm apart. The distance between maxima 2.0 m away is 180 mm. If the speed of the ripples is 25 cm/s, calculate the frequency of the vibrating sources.

6. 6. In a Young’s interference experiment, the two slits are
separated by mm and the incident light includes
two wavelengths: 1 = 510 nm (green) and 2 = 430 nm
(blue). The overlapping interference patterns are observed
on a screen 1.50 m from the slits. Calculate the minimum
distance from the center of the screen to a point where
a bright fringe of the green light coincides with a bright
fringe of the blue light.

7. 7. Measurements are made of the intensity distribution within
the central bright fringe in a Young’s interference pattern. At a particular value of y, it is found that I/Imax = 0.90 when 600-nm light is used. What wavelength of light should be used to reduce the relative intensity at the same location to 64.0% of the maximum intensity?

8. 8. Consider the double-slit arrangement shown in Figure, where the slit separation is d and the distance from the slit to the screen 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’.

9. 9. A thin film of oil (n = 1.25) is located on smooth, wet pavement.
When viewed perpendicular to the pavement, the
film reflects most strongly red light at 640 nm and reflects
no green light at 512 nm. How thick is the oil film?
10. A possible means for making an airplane invisible to radar
is to coat the plane with an antireflective polymer. If radar
waves have a wavelength of 3.00 cm and the index of refraction of the polymer is n = 1.50, how thick would you make the coating?

10. 11. An oil film (n = 1.45) floating on water is illuminated
by white light at normal incidence. The film is 280 nm thick. Find (a) the wavelength and color of the
light in the visible spectrum most strongly reflected and
(b) the wavelength and color of the light in the spectrum most strongly transmitted. Explain your reasoning.

11. 12. A beam of 580-nm light passes through two closely spaced glass plates at close to normal incidence as shown in Figure. For what minimum nonzero value of the plate separation d is the transmitted light bright?

12. 13. An air wedge is formed between two glass plates separated at one edge by a very fine wire of circular cross section as shown in Figure. When the wedge is illuminated
from above by 600-nm light and viewed from above,
30 dark fringes are observed. Calculate the diameter d of
the wire.

13. 14. Two glass plates 10.0 cm long are in contact at one end and
separated at the other end by a thread with a diameter d =
mm. Light containing the two wavelengths 400 nm and 600 nm is incident perpendicularly and viewed by reflection. At what distance from the contact
point is the next dark fringe?

14. 15. When a liquid is introduced into the air space between the lens and the plate in a Newton’s-rings apparatus, the diameter of the tenth ring changes from 1.50 to 1.31 cm. Find the index of refraction of the liquid.

15. 16. In a Newton’s-rings experiment, a plano-convex glass (n =
1.52) lens having radius r = 5.00 cm is placed on a flat plate
as shown in Figure. When light of wavelength =
650 nm is incident normally, 55 bright rings are observed,
with the last one precisely on the edge of the lens. (a) What
is the radius R of curvature of the convex surface of the
lens? (b) What is the focal length of the lens?

16. INTERFERENCE FROM THIN FILMS
Problem: SP 41-4
Lenses are often coated with thin films of transparent substances such as MgF2 (n=1.38) to reduce the reflection from the glass surface. How thick a coating is required to produce a minimum reflection at the center of the visible spectrum? ( wavelength = 550nm)
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17. INTERFERENCE FROM THIN FILMS
Problem: E 41-23
A disabled tanker leaks kerosene (n=1.20) into the Persian Gulf, creating a large slick on top of water (n = 1.33).
If you look straight down from aeroplane on to the region of slick where thickness is 460nm, for which wavelengths of visible light is the reflection is greatest?
If you are scuba diving directly under this region of slick, for which wavelengths of visible light is the transmitted intensity is strongest?
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18. INTERFERENCE FROM THIN FILMS
Problem: E 41-25
If the wavelength of the incident light is λ = 572 nm, rays A and B in Fig are out of phase by λ. Find the thickness d of the film.
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19. INTERFERENCE FROM THIN FILMS
Problem: E 41-29
A broad source of light (wavelength = 680nm) illuminates normally two glass plates 120 mm long that touch at one end and are separated by a wire 0.048mm in diameter at the other end. How many bright fringes appear over 120 mm distance?
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20. INTERFERENCE FROM THIN FILMS
Problem: E41-33
In a Newton’s ring experiment, the radius of curvature R of the lens is 5.0m and its diameter is 20mm.
How many ring are produced?
How many rings would be seen if the arrangement is immersed in water (n = 1.33)?
(Assume wavelength = 589nm)
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21. MICHELSON’S INTERFEROMETER
Problem: SP 41-6
Yellow light (wavelength = 589nm) illuminates a Michelson interferometer. How many bright fringes will be counted as the mirror is moved through 1.0 cm?
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22. MICHELSON’S INTERFEROMETER
Problem: E41-40
An airtight chamber 5.0 cm long with glass windows is placed in one arm of a Michelson’s interferometer as indicated in Fig Light of wavelength λ = 500 nm is used. The air is slowly evacuated from the chamber using a vacuum pump. While the air is being removed, 60 fringes are observed to pass through the view. From these data find the index of refraction of air at atmospheric pressure.
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