PH 103 Dr. Cecilia Vogel Lecture 10

Review Outline  diffraction  breakdown of ray model  special case: single slit  resolution  Lenses  multiple lenses  application to microscope  application to telescope

Recall Ray Model  Light travels in a straight line  except when it strikes a new material  Works very well for all waves  whenever wavelength << sizes of obstacles and openings  Examples  light through a window or open door  satellite signal approaching earth  “line-of-sight“

Diffraction  Ray model breaks down for all waves  whenever wavelength  sizes of obstacles and openings  Wave diffracts - bends, changes direction through opening, or around obstacle  Examples  sound through open door  radio wave around building  visible light thru very small slit  not line-of-sight

Ray Model vs. Diffraction house Sound acts as a wave. Diffracts as it passes near house. I hear sound from behind house. TOP VIEWS house Light acts as a ray. Travels straight past house. I cannot see behind house. Sound’s wavelength is similar to size of house. Light’s wavelength is much smaller than house.

Single Slit Diffraction  What if you had two houses?  the wave would bend  both ways.  The wave would  spread out.  This spreading is called diffraction. house

Single Slit diffraction pattern  Width of central bright spot angular widthwidth  =2 /W (radians)  y=2 L/W (distance) source what you see on a screen slit width =W  yy L

Single Slit diffraction pattern  Width of central bright spot  How does pattern depend on  slit width, W?  narrower slit causes more diffraction & wider pattern  =2 /W (radians)  y=2 L/W (distance)

Single Slit diffraction pattern  Width of central bright spot  How does pattern depend on  wavelength,   longer wavelengths diffract more  Helps explain why sky is blue & sunset red  Long- red is more likely to diffract around air molecules (We see more red in approx dir of sun)  Short- blue is more likely to scatter off of air molecules (We see more blue in sky away from sun)  =2 /W (radians)  y=2 L/W (distance)

Resolution  Width of central bright spot. Recall:  narrower opening causes more diffraction & wider bright spot…  the light is blurred over a larger spot  less clear!  This is true of all shape openings, including round ones  Resolution of a microscope or telescope depends on size of the lenses!  lens diameter  That’s the opening the light diffracts through

Resolution  Resolution of a microscope or telescope depends on diameter of the lenses, D.  The smaller the lens, the more diffraction,  thus the more blurring of image.   res =“Rayleigh Criterion”  is an angular size  RP = “Resolving power”  is a size  Both indicate the smallest you can see without too much blurring due to diffraction  res =1.22 /DRP=1.22 f obj /D