Interference

Constructive and Destructive Interference

Huygen's Construction

• Every point on a wavefront is a source of wavelets.

Diffraction

• Spreading of waves after they travel around obstacles or through apertures.

Multiple Choice

Which property of waves does this illustrate?

• Interference

• Reflection

• Refraction

• Diffraction

Multiple Choice

We can see the diffraction in the harbors. What happen with the wavelength in diffraction?

• Increase

• Not change

• Decrease

Multiple Choice

Diffraction also occurs in telecommunication system in a mountain area as illustrated in picture. What happen with the wave speed when diffraction occurs?

• Increase

• Not change

• Decrease

Interference

• Situations where waves from a small number of sources travel different paths and arrive at an observer with different phases.

Multiple Choice

If you use 2 flashlight together, what pattern you will see?

• The intensity of light will be larger

• There will be dark-light pattern

Incoherent Sources

• Waves from independent sources

• Do not maintain a fixed phase relationship with each other.

• We cannot accurately predict the phase

• Rapidly fluctuating phase relationships.

Coherent Waves

• Coherent waves must be locked in with a fixed phase relationship.

• 
  

• 
  

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Multiple Choice

Which source will produce an interference?

• Incoherent source

• Coherent source

Multiple Choice

What is the name of this phenomena?

• Constructive interference

• Destructive interference

• Reflection

• Refraction

Multiple Choice

What is the name of this phenomena?

• Constructive interference

• Destructive interference

• Reflection

• Refraction

Multiple Choice

Which one is constructive interference?

• Point A

• Point B

Double-slit Interference

• Explain the pattern in the picture beside!

Double-slit Interference

Double slit Interference Equation

• Maxima: $d\ \sin\ \theta\ =\ n\lambda$  

• Minima:  $d\ \sin\ \theta\ =\ \left(n+\frac{1}{2}\right)\lambda$  

Example

A laser (λ = 690.0 nm) is used to illuminate two parallel slits. On a screen that is 3.30 m away from the slits, interference fringes are observed. The distance between adjacent bright fringes in the center of the pattern is 1.80 cm. What is the distance between the slits? (0.127 mm)

Multiple Choice

Monochromatic light falling on two slits 0.018 mm apart produces the fifth-order bright fringe at an 8.6° angle. What is the wavelength of the light used?

• 540 nm

• 270 nm

• 810 nm

Multiple Choice

The third-order bright fringe of 610-nm light is observed at an angle of 31° when the light falls on two narrow slits. How far apart are the slits?

• 3.6 x 10^-6 m

• 1.8 x 10^-6 m

• 5.4 x 10^-6 m

Multiple Choice

Monochromatic light falls on two very narrow slits 0.048 mm apart. Successive fringes on a screen 6.50 m away are 8.5 cm apart near the center of the pattern. Determine frequency of the light!

• 4.8 x 10¹⁴ Hz

• 2.4 x 10¹⁴ Hz

• 1.2 x 10¹⁴ Hz

Path Difference

Gratings

• Maxima:

   $d\ \sin\ \theta\ =\ m\ \lambda$  

• Where:  $d\ =\ \frac{1}{N}$  

• N = number of slits per cm

• d = distance between each slits

Multiple Choice

A grating has exactly 8000 slits uniformly spaced over 2.54 cm and is illuminated by light from a mercury vapor discharge lamp. What is the expected angle for the third-order maximum of the green line (λ = 546 nm)?

• 31^o

• 52^o

• 14^o

Multiple Choice

A red line (wavelength 630 nm) in the third order overlaps with a blue line in the fourth order for a particular grating. What is the wavelength of the blue line?

• 470 nm

• 630 nm

• 550 nm

Single slit diffraction

Explain what pattern you see in the picture beside and the difference with double slit interference!

Pattern in Single-Slit Diffraction

Single slit diffraction equation

• Minimum interference formula:

•  $d\ \sin\ \theta\ =\ n\ \lambda$  

•  $d\ \frac{y}{L}=n\ \lambda$  

How a CD is read?