1. Physics 1B03summer-Lecture 11 Interference of Light Light is an electromagnetic (EM) wave. Wave properties: Diffraction – bends around corners, spreads out from narrow slits Interference – waves from two or more coherent sources interfere

2. Physics 1B03summer-Lecture 11 Double Slit Result: Many bright “fringes” on screen, with dark lines in between. screen double slit separation d θ m=2 m=1 m=0 (center) m=-1 m=-2 incident light

3. Physics 1B03summer-Lecture 11 A very thin transparent sheet placed over BOTH slits delays the waves passing through both slits by one-quarter cycle. What happens? A)The interference fringes disappear B)The fringes all shift upwards C)The fringes all shift downwards D)There is no change to the pattern. Concept Quiz

4. Physics 1B03summer-Lecture 11 Example A double slit interference patter is observed on a screen 1.0m behind two slits spaced 0.3mm apart. Ten bright fringes span a distance of 1.65 cm. What is the wavelength of light used ?

5. Physics 1B03summer-Lecture 11 Individual waves (one slit open at a time), I 1 = I 2 = I o where I o = (constant) x E o 2 Both slits open: Intensity:

6. Physics 1B03summer-Lecture 11 Notes: 1)Maximum I R is 4 x I O. This is twice as large as the intensity “should” be (in the absence of interference). 2)At the minima, adding the second wave reduces the resultant intensity to zero, instead of doubling it. Averaged over the entire pattern, the total energy does add up to the sum of the energies in the individual beams.

7. Physics 1B03summer-Lecture 11 Refractive Index material refractive index speed of light vacuum1c  300,000 km/s air1.0003 glass about 1.5 200,000 km/s water 1.333 225,000 km/s diamond2.4 125,000 km/s The speed of light depends on the material. We define the refractive index “ n ” as n = (speed of light in vacuum)/(speed of light in a material)

8. Physics 1B03summer-Lecture 11 A beam of yellow light (wavelength 600 nm), travelling in air, passes into a pool of water. By what factor do the following quantities change as the beam goes from air into water? A)speed B)frequency C)wavelength

9. Physics 1B03summer-Lecture 11 Reflection and Phase Change Light waves may have a 180° phase change when they reflect from a boundary: “optically dense” medium (larger refractive index) no phase change at this reflection 180° phase change when reflecting from a denser medium Just remember this : low to high, phase shift of pi !

10. Physics 1B03summer-Lecture 11 Example: Thin film What is the minimum thickness of a soap film (n  1.33) needed to produce constructive interference for light with a 500nm wavelength ? (air : n  1.00). What about destructive interference ?

11. Physics 1B03summer-Lecture 11 Example: Antireflection coatings To reduce reflections from glass lenses (n  1.5), the glass surfaces are coated with a thin layer of magnesium fluoride (n  1.38). What is the correct thickness of the coating for green light (550 nm vacuum wavelength)? MgF 2 air glass