LECTURE 12 INTERFERENCE OF LIGHT. Instructor: Kazumi Tolich

Transcription

1 LECTURE 12 INTERFERENCE OF LIGHT Instructor: Kazumi Tolich

2 Lecture The interference of light Young s double-slit experiment Analyzing double-slit interference 17.3 The diffraction grating Spectroscopy Reflection gratings

3 17.2 The interference of light Because light acts as a wave, light waves can diffract interfere.

4 Quiz: For two identical rays of light to interfere destructively, their path lengths A. must be equal. B. must differ by an odd number of half wavelengths. C. must differ by an integer number of wavelengths.

5 Quiz: answer must differ by an odd number of half wavelengths If the sources are in phase, constructive and destructive interferences satisfy r = mλ m = 0,1,2, (constructive) 4λ r = m + -. λ m = 0,1,2, (destructive) 5λ 4λ 4.5λ

6 17.2 Young s double-slit experiment / Demo Double-slit experiment with light passing through a double slit striking a viewing screen demonstrated the wave nature of light. The interference fringes, an alternating pattern of bright and dark fringes, are due to the path length difference. The central maximum is the brightest fringe at the midpoint of the screen. Demo: Laser and double-slits d0

7 17.2 Analyzing double-slit interference 7 The interference patterns are given by d sin θ 4 = mλ d sin θ 4 = m + -. m = 0, 1, 2, (bright) λ (dark) Linear distance from the central maximum: y = L tan θ

8 17.2 Analyzing double-slit interference small θ 8 Under the small angle approximation, the interference equations become θ 4 = m : ; θ 4 = m + -. m = 0, 1, 2, : and y 4 = 4:< ; ; and y 4 = = m + -. :< ; (bright) (dark) The fringe spacing is y = λl d

9 Quiz: A laboratory experiment produces a double-slit interference pattern on a screen. What is difference in the path-lengths from the slits to the point on the screen marked with a dot in terms of the wavelength λ? Enter a number.

10 Quiz: answer The bright fringes are due to constructive interference. The constructive interference occur when the path-length difference is an integer multiple of λ. r = 0 r = λ r = 2λ r = 1 2 λ r = 3 2 λ r = 5 2 λ

11 Quiz: A green laser light produces a double-slit interference pattern on a screen. Which of the following changes can cause the fringes to move closer together if only one change is made at a time? Choose all that apply. A. The screen is moved farther away. B. The screen is moved closer. C. A red laser is used instead. D. A blue laser is used instead. E. The slits are moved closer together. F. The slits are moved farther apart.

12 Quiz: answer The fringes would move closer together if The screen is moved closer. L is smaller. A blue laser is used instead. A blue laser has a smaller λ. The slits are moved farther apart. d is larger. The fringe spacing is given by y = :< ;.

13 Quiz: In a double-slit experiment, the two slits are separated by a distance equal to 3.5 times the wavelength of light shining on them. How many bright fringes can you see?

14 Quiz: answer 14 7 Bright fringes occur where there are constructive interference of rays from the slits. Constructive interference: d sin θ 4 = mλ, m = 0, 1, 2, 3 (bright) sin θ 4 = m : = m : = 4, m = 0, 1, 2, 1, m = 0, 1, 2, 3, but not 4, 5. Since 1 sin θ = For m = 1, 2, 3, there are two bright fringes on both sides of the central maximum.

15 Example: In a double-slit arrangement, the slits are separated by a distance equal to 100 times the wavelength of the light passing through the slits. a) What is the angular separation in radians between the central maximum and an adjacent maximum? b) What is the distance between these maxima on a screen 50 cm from the slits?

16 17.3 The diffraction grating The light waves from a diffraction grating will all be in phase with each other for each order of diffraction m d sin θ 4 = mλ and y 4 = L tan θ 4, m = 0, 1, 2,

17 Quiz: In a laboratory experiment, a diffraction grating produces an interference pattern on a screen. What happens if the number of slits in the grating is increased, with everything else (including the slit spacing) the same? Choose all that apply. A. The fringes stay the same brightness. B. The fringes get brighter and narrower. C. The fringes get dimmer and wider. D. The fringes get closer together. E. The fringes get farther apart. F. The fringes stay in the same positions.

18 Quiz: / Demo If the number of slits in the grating is increased, the fringes get brighter and narrower and stay in the same positions. The bright fringes occur at d sin θ 4 = mλ and y 4 = L tan θ 4, m = 0, 1, 2,, independent of the number of slits. Demo: Laser and multi-slits

19 Quiz: White light passes through a diffraction grating and forms rainbow patterns on a screen behind the grating. For each rainbow: A. The red side is on the left, and the violet side is on the right; B. The red side is on the right, and the violet side is on the left; C. The red side is closest to the center of the screen, and the violet side is farthest from the center of the screen. D. The red side is farthest from the center of the screen, and the violet side is closest to the center of the screen.

20 Quiz: answer / Demo The red side is farthest from the center of the screen, and the violet side is closest to the center of the screen. d sin θ 4 = mλ, m = 0, 1, 2, The longer the wavelength λ, the larger the angle θ for a given diffraction grating with a fixed d. Demo: Diffraction gratings Dispersion of white light

21 17.3 Spectroscopy Spectroscopy is the science of measuring the well-defined wavelengths of atomic and molecular emissions due to their excitation by light, electricity, or collisions. If the light incident on a grating consists of two slightly different wavelengths, they will diffract at slightly different angles.

22 17.3 Reflection gratings The interference pattern of reflection gratings is exactly the same as the pattern of light transmitted through transmission gratings of the same rulings. Some of the colors of bird feathers, butterfly wings, insect shells do not come from pigment, but from a series of parallel ridges which diffract light.

23 Example: (Knight P17.54) 23 The wings of some beetles have closely spaced parallel lines of melanin, causing the wing to act as a reflection grating. Suppose sunlight shines straight onto a beetle wing. If the melanin lines on the wings are spaced 2.0 μm apart, what is the first order diffraction angle for green light (λ = 550 nm)?