chapter 34 the wave nature of light; interference

Chapter 34The Wave Nature of Light;

Interference

33-3 Combinations of LensesExample 33-5: A two-lens system.

Two converging lenses, A and B, with focal lengths fA = 20.0 cm and fB = 25.0 cm, are placed 80.0 cm apart. An object is placed 60.0 cm in front of the first lens. Determine (a) the position, and (b) the magnification, of the final image formed by the combination of the two lenses.

This useful equation relates the radii of curvature of the two lens surfaces, and the index of refraction, to the focal length:

33-4 Lensmaker’s Equation

33-4 Lensmaker’s EquationExample 33-7: Calculating f for a converging lens.

A convex meniscus lens is made from glass with n = 1.50. The radius of curvature of the convex surface is 22.4 cm and that of the concave surface is 46.2 cm. (a) What is the focal length? (b) Where will the image be for an object 2.00 m away?

34-1 Waves versus Particles; Huygens’ Principle and Diffraction

Huygens’ principle: every point on a wave front acts as a point source; the wave front as it develops is tangent to all the wavelets.

34-1 Waves versus Particles; Huygens’ Principle and

Diffraction

Huygens’ principle is consistent with diffraction: The wave bend in behind an obstacle, this is called diffraction

34-1 Waves versus Particles; Huygens’ Principle and Diffraction

34-2 Huygens’ Principle and the Law of Refraction

θ1 θ2

Huygens’ principle can also explain the law of refraction (Snell’s Law).

As the wavelets propagate from each point, they propagate more slowly in the medium of higher index of refraction.

This leads to a bend in the wave front and therefore in the ray.


The frequency of the light does not change, but the wavelength does as it travels into a new medium:


If light is a wave, interference effects will be seen, where one part of a wave front can interact with another part.

One way to study this is to do a double-slit experiment:

34-3 Interference – Young’s Double-Slit Experiment

Monochromatic wavelength (single wavelength) through two slits.

If light is a wave, there should be an interference pattern.


Principle of Superposition

• When waves overlap, their amplitudes addConstructive Destructive

Peaks line up with peaks Peaks line up with troughs

+ +

==

l

l PhaseShifted180°

/2

What are PHASE differences?

Phase difference is a term used to describe the relative alignment of the peaksIN PHASE= two waves are lined up—constructive interferenceOUT of PHASE= one wave is upside down relative to the other—destructive interference

What causes Phase differences?

• Light travels Different distances

Source 1

Source 2

d1

d2

∆d = d1-d2 = m

Constructive Interference when in phase

Where m is an integer

∆d = d1-d2 = (m+1/2)

Destructive Interference when out of phase

Where m is an integer

Path difference is an integral number of wavelengths

Path difference is a half integral number of wavelengths

The interference occurs because each point on the screen is not the same distance from both slits. Depending on the path length difference, the wave can interfere constructively (bright spot) or destructively (dark spot).


Between the maxima and the minima, the interference varies smoothly.


Young’s Double Slit

Light from each slit travels to a screen where the waves

interfere

d = slit separationl = distance to screen

l

d

m = fringe order

m = 0m = +1

m = +2m = -2

m = -1

Phase differences due entirely to path

differences

Young’s Double Slit

m = order = 0, 1, 2, …

l

d

Path difference

Maxima : Constructive Interference- occur where Δd =s2-s1=dsinθ= mY

Minima: destructive Interference- occur where Δd = (m + ½)

http://dev.physicslab.org/asp/applets/doubleslit/Applet:

tan𝜃=𝑦ℓ


Example 34-2: Line spacing for double-slit interference.

A screen containing two slits 0.100 mm apart is 1.20 m from the viewing screen. Light of wavelength λ = 500 nm falls on the slits from a distant source. Approximately how far apart will adjacent bright interference fringes be on the screen?

Since the position of the maxima (except the central one) depends on wavelength, the first- and higher-order fringes contain a spectrum of colors.


Another way path lengths can differ, and waves interfere, is if they travel through different media. If there is a very thin film of material – a few wavelengths thick – light will reflect from both the bottom and the top of the layer, causing interference. This can be seen in soap bubbles and oil slicks.

34-5 Interference in Thin Films

The wavelength of the light will be different in the oil and the air, and the reflections at points A and B may or may not involve phase changes.


If the Path ABC= mλn the two waves reach the eye in phase and (m+1/2) λn if they are out of phase

A similar effect takes place when a shallowly curved piece of glass is placed on a flat one. When viewed from above, concentric circles appear that are called Newton’s rings.



A beam of light reflected by a material with index of refraction greater than that of the material in which it is traveling, changes phase by 180° or ½ cycle.

Example 34-6: Thin film of air, wedge-shaped.

A very fine wire 7.35 x 10-3 mm in diameter is placed between two flat glass plates. Light whose wavelength in air is 600 nm falls (and is viewed) perpendicular to the plates and a series of bright and dark bands is seen. How many light and dark bands will there be in this case? Will the area next to the wire be bright or dark?


Problem Solving: Interference

1. Interference occurs when two or more waves arrive simultaneously at the same point in space.

2. Constructive interference occurs when the waves are in phase.

3. Destructive interference occurs when the waves are out of phase.

4. An extra half-wavelength shift occurs when light reflects from a medium with higher refractive index.


chapter 34 the wave nature of light; interference

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