1. Lecture 26-1 Lens Equation ( < 0 )  True for thin lens and paraxial rays.  magnification m = h’/h = - q/p

2. Lecture 26-2 Signs in the Lens Equation for Thin Lenses p is positive for real object q is positive for real image q is negative for virtual image m is positive if image is upright m is negative if image is inverted f is positive if converging lens f is negative if diverging lens p is negative for virtual object

3. Lecture 26-3 Geometric Optics vs Wave Optics Geometric optics is a limit of the general optics where wave effects such as interference and diffraction are negligible.  Geometric optics applies when objects and apertures involved are much larger than the wavelength of light.  In geometric optics, the propagation of light can be analyzed using rays alone. Wave optics (sometimes also called physical optics) - wave effects play important roles.  Wave optics applies when objects and apertures are comparable to or smaller than the wavelength of light.  In wave optics, we must use the concepts relevant to waves such as phases, coherence, and interference.

4. Lecture 26-4 Coherence  When the difference in phase between two (or more) waves remains constant (i.e., time-independent), the waves are said to be perfectly coherent. Only coherent waves can produce interference fringes! Coherence length: the spatial extent over which light waves remain coherent.  A single light wave is said to be coherent if any two points along the propagation path maintains a constant phase difference. - laser light and light transmitted through a small aperture are coherent. - light from a light bulb and sun light over some area are incoherent.

5. Lecture 26-5 READING QUIZ 1 Which of the following statements is incorrect ? A| Wave optics applies when objects and apertures are comparable or smaller than the wavelength of light. B| Two light waves of different frequency f = c/λ, where λ is the wavelength and c is the light velocity, exhibit interference fringes. C| When the difference in phase of two or more waves remains constant (time independent) the waves are perfectly coherent. D| A LASER is a source of a single frequency perfectly coherent light. E| An incandescent light emits light that has a short (~ 1 meter ) coherence length.

6. Lecture 26-6 Interference of Two Coherent Waves Constructive interference (in phase) Snapshot of wave fronts at a given instant Destructive interference (completely out of phase) B,C A

7. Lecture 26-7 Intensity of Interference Fringes Let the electric field components of the two coherent electromagnetic waves be The resulting electric field component point P is then Intensity is proportional to E 2 I=0 when  = (2m+1) , i.e. half cycle + any number of cycle.

8. Lecture 26-8 Thin Film Thin here means that the thickness is comparable to the wavelength of the light. The reflected light waves from the two sides of a thin film interfere. Phase change by  If the incident light propagates from a medium of lower index of refraction toward one of higher index of refraction, the phase of the reflected wave shifts by π. Phase difference could come from: reflection, path length difference, different indices of refraction Destructive interference eliminates (or minimizes) the reflected light! e.g., non-reflecting lens coating

9. Lecture 26-9 Thin-Film Interference-Cont’d Path length difference: (Assume near-normal incidence.) destructive constructive where ray-one got a phase change of 180 o due to reflection from air to glass. the phase difference due to path length is: then total phase difference:  =  ’+180.

10. Lecture 26-10 DOCCAM 2 OIL FILM INTERFERENCE

11. Lecture 26-11 Thin-Film Continued The previous discussion was for the situation in which n 2 > n 1 and n 2 > n 3, i.e., the index of refraction of the film is larger than those of the surrounding media, but they are also valid if the index of refraction of the film is smaller than those of the surrounding media (n 2 < n 1 and n 2 < n 3 ). The equations fail for some of the following situations. Which one(s)? If the film has an intermediate index of refraction Conditions for maxima/minima will reverse!

12. Lecture 26-12 Warm-up quiz 2 a)The reflection is dark by destructive interference of rays 1 and 2 b) The reflection is bright by constructive interference of rays 1 and 2 c) The reflection is colorful by interference of rays 1 and 2. 2 1 water (n=1.33) oil (n 1 >1.33) Monochrome light of wavelength λ O in air is incident normal to a thin layer of oil film floating on water as shown. If the film thickness is 5λ/(4n 1 ). Which of the following statement is true?

13. Lecture 26-13 Newton’s Rings: The air between the glass plates acts like a thin film. For a small strip of the wedge, the thin-film equations can be used to determine whether constructive or destructive interference of the reflected light occurs. Since the thickness of the film changes over the length of the wedge, alternating bright and dark fringes form, when the wedge is illuminated. A sensitive technique for checking imperfections in a material! “optically flat” Thin-Film Wedge

14. Lecture 26-14 The air between the glass plates acts like a thin film. Since the thickness of the film changes over the radius of the plates, alternating bright and dark fringes form, when the plates are illuminated. Because of the curvature of the upper piece, the film thickness varies more rapidly at larger radius. Thus the fringe separation is smaller toward the outside. Newton’s Ring

15. Lecture 26-15 Two (narrow) slit Interference Upon reaching the screen C, the two wave interact to produce an interference pattern consisting of alternating bright and dark bands (or fringes), depending on their phase difference. Constructive vs. destructive interference According to Huygens’s principle, each slit acts like a wavelet. The the secondary wave fronts are cylindrical surfaces. Young’s double-slit experiment

16. Lecture 26-16 Interference Fringes For D >> d, the difference in path lengths between the two waves is A bright fringe is produced if the path lengths differ by an integer number of wavelengths, A dark fringe is produced if the path lengths differ by an odd multiple of half a wavelength,

17. Lecture 26-17 Intensity of Interference Fringes Let the electric field components of the two coherent electromagnetic waves be The resulting electric field component point P is then Intensity is proportional to E 2 I=0 when  = (2m+1) , i.e. half cycle + any number of cycle.

18. Lecture 26-18 Intensity of Interference Fringes-Cont’d For Young’s double-slit experiment, the phase difference is

19. Lecture 26-19 DOCCAM 2 Laser and slits (small apertures)

20. Lecture 26-20 Physics 241 10:30 Quiz 3 a) λ /(4n 1 ) b) λ /4 c) λ /(2n 1 ) d) λ /2 e) 3λ /4 2 1 glass (n 1 >1) Light of wavelength λ in air is incident normal to a thin layer of glass held in air as shown. If the reflection is suppressed (dark) by interference of rays 1 and 2, what is a possible thickness d of the glass layer?

21. Lecture 26-21 Physics 241 11:30 Quiz 3 a) λ /(4n 1 ) b) λ /4 c) λ /(2n 1 ) d) λ /2 e) 3λ /4 2 1 water (n=1.33) oil (n 1 >1.33) Light of wavelength λ in air is incident normal to a thin layer of oil film floating on water as shown. If the reflection is suppressed (dark) by interference of rays 1 and 2, what is a possible thickness d of the oil film?

22. Lecture 26-22 Physics 241 Quiz 3 a) λ /(4n 1 ) b) λ /4 c) λ /(2n 1 ) d) λ /2 e) 3λ /4 2 1 water (n=1.33) oil (n 1 >1.33) Light of wavelength λ in air is incident normal to a thin layer of oil film floating on water as shown. If the reflection is bright (constructive interference) by interference of rays 1 and 2, what is a possible thickness d of the oil film?