Try This
Radiation of 400 nm passes through two slits.  Given the angle of diffraction for the second order dark fringe of 0.095o, determine the slit separation.  Show the calculation and check your answer with the simulation. (3.6 x 10 -4 m)


Read
As you will have noticed from each of the scenarios, the angle of diffraction is always very small, making it difficult to measure accurately in many experimental conditions.  In such cases, a second equation is used that approximates the small angle using a ratio of the distance separating the screen and slits to the distance between any two antinodes.  For very small angles, use the equation sin Î¸ = x / L .  Read the " infoBIT" on page 690 of your textbook for the derivation of the small angle approximation.

The interference pattern produced by diffraction through a double slit can be analyzed using the following equation.

 

λ=xdnl

 

Quantity

Symbol

SI Unit

wavelength

λ

m

distance from central antinode to antinodal line

x

m

slit spacing (separation)

d

m

path difference*

n

none (number of wavelengths)

distance between slits and screen

L

m

 








* Constructive interference (antinodes − bright fringes) occurs when the path difference is a whole number of wavelengths ( n = 0, ±1, ±2, ...). Thus, for antinodes or bright fringes:  n = 1, 2, 3, 4, ....

* Destructive interference (nodes − dark fringes) occurs when the path difference is offset by half a wavelength ( n = ±0.5, ±1.5, ±2.5, ...). Thus, for nodes or dark fringes:   n = 0.5, 1.5, 2.5, 3.5, ....

 


Try This
Review "Example 13.9" on page 691 of the textbook then complete "Practice Problems" 1-3 on page 691.
 

The tightly spaced concentric rings on the CD/DVD from page one of this lesson are an example of a  diffraction grating . 

 

The equations that describe two-slit experiments are equally useful for gratings because they only rely on the spacing between any two slits.  Dividing the width of the grating by the total number of lines or spaces on the grating gives the distance between any two lines, which is the slit separation that can be used with any diffraction equation.


Diffraction Grating:  an optical component that has a surface covered by a regular pattern of parallel lines or grooves that are usually separated by a distance comparable to the wavelength of light.


Read
Read "Diffraction Gratings" and "Example 13.10" on pages 692-693 of your textbook.


Try This
Complete "Practice Problems" 1-3 on page 693 of the textbook.   NOTE : The answer to Practice Problem 1 is wrong.  Because the angle is larger than 10 degrees, the formula with the sin must be used.   This correct answer is 5.94 x 10 -7 m.


Read & Do
Read "Inquiry Lab" on pages 694-695 of the textbook then complete "Analysis" questions 1 to 4 on page 695 using the results below.

Light

Left

Right

Red

0.214 m

0.209 m

Green

0.150 m

0.152 m

Blue

0.135 m

0.139 m

       

Read and Watch
The purpose of Thomas Young's experiment was to demonstrate the wave nature of light.  Polarization gave further evidence to support the wave model of light.  Read pages 695-696 of your textbook to find out about polarization. Then view the animation Polarization.


Self-Check

Answer the following self-check (SC) questions then click the "Check your work" bar to assess your responses.

 

SC 5.  

What part of an electromagnetic wave does the polar filter affect?

 

SC 6.

Polarized sunglasses are popular with people who fish and drive boats.  Why are polarized sunglasses popular with those groups of people?

 

SC 7.  

The liquid crystal display (LCD) used on calculator screens, cellular phones, MP3 players, LCD TVs, and computer projectors use polar filters to block some colours and let other colours be projected onto the screen.  What is a possible problem if you wear polarized sunglasses and attempt to use an LCD product?

 

    Self-Check Answer

Contact your teacher if your answers vary significantly from the answers provided here.

 

SC 5.  

The polar filter absorbs the electric field; however, you can't have a magnetic field without an electric field so the wave is stopped by the filter when the electric field is not parallel to the slits of the filter.

 

SC 6.  

The polar filter absorbs the horizontally polarized light reflected from the water that causes the most irritating glare. Without the glare, it is much easier to see what is under the water, be it a submerged hazard or a fish. Avoiding glare causes less eyestrain when outside near reflective surfaces.

 

SC 7.  

If the polar lens on the sunglasses lines up at 90° to the polar filter in the LCD, then the picture could be colour distorted or completely invisible.