Friday 18 Mar

 

 

 

Index of Refraction: 

  • The lower the number the faster it goes

  • n = 1 in air or vacuum

  • water: n = 1.333

  • n = c/v   (3x108) / velocity in that substance

 

Recall:

Frequency doesn't change when going from one medium to another.

(but both l & V changes)

 

n = c/v    

v = fl

When light (or waves in general) reflect off an object, they phase shift 1800 on the reflection.

 

Question: What is the minimum depth of a oil sheen that reflects max intensity of red light:

Given:

  •  red l = 700 nm    (i.e., x 10-9m)
  • n = 2.0

 

 

 

 

 

 

answer:

Phase shift is 1800, so thickness (t) must be a multiple of 1/2 l.

The wave must travel there and back and be in phase

i.e., 2t = 1/2 l --> t = 1/4 l

 

v = fl --> f = v/l

(n = c/voil ) --> so,     voil = (c/noil)

foil  =  fair   -->    voil/loil  =  vair/lair

 (c/noil) / loil = c / lair

--> (1/noil) / loil = 1/ lair

 -->  loil  =  lair /  noil

loil  =  700 x 10-9 /  2  =  350 x 10-9 m

  t = (1/4)loil

    t =  350 x 10-9 /4 = 87.5 x 10-9 m

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Young's Double Slit Experiment

x =  mlL /d

The formula that we will use to figure out problems involving double slit experiments is easy to mix up, so make sure you study it carefully.

 

 

λ = wavelength of light used (m)
         x=distance from central fringe (m)
d = distance between the slits (m)

m = the order of the fringe

                                 L = length from the screen with slits to the viewing screen (m)

Figure 5

It is very easy to mix up the measurements of x, d, and L.

  • Make sure to look at Figure and see the different things each is measuring.

 

 

There is also a version of the formula where you measure the angle between the central fringe and whatever fringe you are measuring.

d sin q = ml

  • The formula works the same way, with the only difference being that we measure the angle instead of x and L.

 

Example 1: A pair of screens are placed 13.7m apart. A third order fringe is seen on the screen 2.50cm from the central fringe. If the slits were cut 0.0960 cm apart, determine the wavelength of this light. Roughly what color is it?

Just to make sure you’ve got all the numbers from the question matched with the correct variables…

L = 13.7 m
m = 3
x = 2.50cm = 0.0250 m
d = 0.0960cm = 9.60e-4 m

 

 

 

 

 

x =  mlL /d

0.025 = 3l(13.7m) / (9.6x10-4m)

 l= (0.25)(9.6x10-4m) / 3(13.7m)

l= 584 x10-9 m     or  584nm

 

It’s probably a yellow light being used given the wavelength we've measured.

 

 

 

 

 

Single-slit diffraction

http://www.physics.uoguelph.ca/applets/Intro_physics/kisalev/java/slitdiffr/index.html

 

  • If waves fronts meet crest to crest or trough to trough they will be in sync, but if they meet crest to trough they will be out of sync.
  • Being in sync will result in constructive interference, while meeting out of sync will result in destructive interference.
  • The result is the same interference pattern, although the effect isn’t nearly as dramatic or clear as the double slit experiment.
    • After the first couple of fringes (n = 1 and 2), the edges start getting really fuzzy, so you have a hard time measuring anything.
  • The only real difference in calculations is that "d" is now the width of the single opening.

  • Example:  Determine how far from the central fringe the 1st order violet (λ = 350nm) and red (λ = 700nm) colors will appear if the screen is 10 m away and the slit is 0.050 cm wide.

     

     

    For the violet light…(λ = 350nm)

    x =  mlL /d

    x = 350 x10-9 m (1)(10m) / (0.0005m)

      x = 0.007m

     
    For the red light…(λ = 700nm)

     

    x =  mlL /d

    x = 700 x10-9 m (1)(10m) / (0.0005m)

      x = 0.014m

     

    For the red light…

     

     

     

    Free Response Day