INTERFERENCE 1 1 The double slit arrangement is

INTERFERENCE 1

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

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. 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=3 m=2 m=1 m=0 m=1 m=2 m=3

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. In a Young’s interference experiment, the two slits are separated by 0. 0250 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. 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. 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. 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?

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.

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?

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.

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 = 0. 050 0 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?

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.

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?

INTERFERENCE FROM THIN FILMS Problem: SP 41 -4 Lenses are often coated with thin films of transparent substances such as Mg. F 2 (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 = 550 nm) MIT-MANIPAL BE-PHYSICS- INTERFERENCE-2010 -11 16

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). (a)If you look straight down from aeroplane on to the region of slick where thickness is 460 nm, for which wavelengths of visible light is the reflection is greatest? (b)If you are scuba diving directly under this region of slick, for which wavelengths of visible light is the transmitted intensity is strongest? MIT-MANIPAL BE-PHYSICS- INTERFERENCE-2010 -11 17

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 41 -24 are out of phase by 1. 50 λ. Find the thickness d of the film. MIT-MANIPAL BE-PHYSICS- INTERFERENCE-2010 -11 18

INTERFERENCE FROM THIN FILMS Problem: E 41 -29 A broad source of light (wavelength = 680 nm) illuminates normally two glass plates 120 mm long that touch at one end are separated by a wire 0. 048 mm in diameter at the other end. How many bright fringes appear over 120 mm distance? MIT-MANIPAL BE-PHYSICS- INTERFERENCE-2010 -11 19

INTERFERENCE FROM THIN FILMS Problem: E 41 -33 In a Newton’s ring experiment, the radius of curvature R of the lens is 5. 0 m and its diameter is 20 mm. (a) How many ring are produced? (b) How many rings would be seen if the arrangement is immersed in water (n = 1. 33)? (Assume wavelength = 589 nm) MIT-MANIPAL BE-PHYSICS- INTERFERENCE-2010 -11 20

MICHELSON’S INTERFEROMETER Problem: SP 41 -6 Yellow light (wavelength = 589 nm) illuminates a Michelson interferometer. How many bright fringes will be counted as the mirror is moved through 1. 0 cm? MIT-MANIPAL BE-PHYSICS- INTERFERENCE-2010 -11 21

MICHELSON’S INTERFEROMETER Problem: E 41 -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 41 -28. 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. MIT-MANIPAL BE-PHYSICS- INTERFERENCE-2010 -11 22