midterm 3, overviewlight as waves (22)examplereflection/refraction (22)Slide 5mirrors and lenses: general (23)PowerPoint PresentationSlide 8Slide 9Slide 10interference (24)double-slit experimentSlide 13reflection & interference(24)thin layersSlide 16single-slit diffraction(24)Slide 18diffraction gratingSlide 20polarization (24)Slide 22optical instruments (25)Slide 24simple magnifier (25)microscope (25)telescope (25)rayleigh’s criterion (25)Slide 29relativity (26)Slide 31Relativistic addition of velocities (26)Slide 33Slide 34Slide 35midterm 3, overviewPHY232Remco [email protected] W109 – cyclotron buildinghttp://www.nscl.msu.edu/~zegers/phy232.htmlThis overview highlights the key points of the material.It is not necessarily complete; you should judge what additional material should be on your equation sheet.PHY232 - Remco Zegers - 2light as waves (22)in vacuum, the speed of light is 3x108 m/sin any other substance: vlight=c/n with n the index of refraction of the materialnair = 1.003 (nearly like vacuum)v=f with : wavelength, f: frequencyI=Psource/(4R2) I: intensity (W/m2) Psource :power of source. R distance from sourcePHY232 - Remco Zegers - 3exampleLight with a wavelength of 600 nm (in water) travels from water (n=1.33) to glass (n=1.5). What are the wavelength, frequency and speed of light in the water and in the glass?In water:v=c/n=3x108/1.33=2.26x108 m/s=600x10-9 m (given)f=v/=3.77x1014 HzIn glass:v=c/n=3x108/1.5=2x108 m/sf: remains unchanged!! = 3.77x1014 Hz=v/f=2x108/3.77x1014=5.30x10-7 mPHY232 - Remco Zegers - 4reflection/refraction (22)reflection:1=rrefraction:Snell’s law: n1sin1=n2sin2two cases: 1) n1< n2: 1> 2 and no total internal reflection (but some reflection can happen)2) n1>n2: 1< 2 but if sin1>n2/n1 total internal reflection will take place and =sin-1(n2/n1) is called the critical angle1 r2n1n21 r2n1n2n1<n2n1>n2PHY232 - Remco Zegers - 5examplelight travels from glass (n=1.5) to air (n=1) under an angle of 400. What is the angle of refraction? is there an incident angle for which total internal reflection will take place? If so, what is the critical angle?Snell’s law: n1sin1=n2sin2 n1=1.5 n2=1 1=400 so 2=74.60since n1>n2 total internal reflection can take place and the critical angle is sin-1(n2/n1)=41.80PHY232 - Remco Zegers - 6mirrors and lenses: general (23)p: object distance (we always choose this +)q: image distance (can be + or -)f: focal length (can be + or -)lens/mirror equation: 1/p+1/q=1/f note: use of signs is different for mirrors or lensesvirtual image: light is NOT actually passing through the imagemagnification M=-q/p=(size of image)/(size of object)negative if inverted (upside-down relative to object)|M| < 1 : image is smaller than object|M| > 1 : image is larger than objectPHY232 - Remco Zegers - 7Mirrors: an overview (23)mirror equation 1/p + 1/q = 1/f f=R/2 where R is the radius of the mirrormagnification: M=-q/p q negative means: image is on other side of mirror than objects type p? image image directionM q fconcave p>f real inverted |M|>0 M -+ +concave p<f virtual not inverted|M|>1 M +- +convex p>|f| virtual not inverted|M|<1 M +- -convex p<|f| virtual not inverted|M|<1 M +- -PHY232 - Remco Zegers - 8examplean object is placed at a distance of two times the focal length in front of a convex mirror. If the focal length is –5 cm, what is the magnification?1/p+1/q=1/ff=-5 cm, p=10 cm, so 1/q=1/(-5)-1/10=-0.3q=-3.33 cmM=-q/p=-(-3.33)/10.=0.33The image is virtual (q is negative, I.e. on the other side of the mirror as the object), upright (M+) and demagnified (|M|<1).PHY232 - Remco Zegers - 9lenses, an overview (23)type p? image image directionM q fconverging p>f real inverted |M|>0 M -+ +convergingp<f virtual not inverted|M|>1 M +- +divergingp>|f| virtual not inverted|M|<1 M +- -divergingp<|f| virtual not inverted|M|<1 M +- -mirror equation 1/p + 1/q = 1/f magnification: M=-q/p lens makers equation: 1/f=(n-1)(1/R1-1/R2)q negative: on same side of the lens as objectdifferent meaningthan for mirrorsPHY232 - Remco Zegers - 10examplean object is placed in front of a lens. An image is created that is situated on the same side of the lens as the object and that is larger than the object. Is the lens converging or diverging?the image must be virtual (same side as object). This still allows both types of lenses. But a diverging lens must have |M|<1 (I.e. image smaller than the object) so that the lens must be converging.PHY232 - Remco Zegers - 11interference (24)constructive interference: path length difference between two sources: m with m=0,1,2…destructive interference: path length difference between two sources: (m+1/2) with m=0,1,2…constructivedestructivePHY232 - Remco Zegers - 12double-slit experimentif small: =sin=tan : radians!!constructive: ym=mL/d destructive: ym=(m+1/2)L/dif not small (but can also be used if is small): constructive: dsin=m & tan=y/Ldestructive: dsin=(m+1/2) & tan=y/LLconstructive: dsin=mdestructive: dsin=(m+1/2)m=0,1,2,3…constructive: bright fringe/maximadestructive: dark fringe/minima follows fromPHY232 - Remco Zegers - 13examplethe distance between the central maximum and first minimum in the interference pattern created by a double slit system is 1 cm. If the distance between the slits and the screen is 10 cm, what is the slit distance d? Given, =550 nmcentral maximum: y=0first minimum: dsin=1/2 m=0tan=y/L=1/10 so =5.71od=0.5 x 550x10-9/sin(5.71)=2.76x10-6 m (2.76 micrometer)PHY232 - Remco Zegers - 14reflection & interference(24)remember that the wavelength of light in a medium with index of refraction n is is vacuum/n1 2n1<n21/2 phase changen1>n21 2no phase changePHY232 - Remco Zegers - 15thin layersconstructive interference between ray 1 and 2: a procedure:if no phase shifts occur at boundaries a-b and b-c (na>nb>nc): 2d=mbif phase shift occurs at boundary a-b only (na<nb nb>nc): 2d=(m+1/2)bif phase shift occurs at boundaries a-b and b-c (na<nb nb>nc): 2d=mbdestructive interference between ray 1 and 2: a procedure:if no
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