Wave Optics

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Young’s Double-Slit Experiment

Light is incident onto two slits and after passing through them strikes a screen

The light intensity on the screen shows an interference pattern

If the slits are separated by a distance d, then the difference in length between the paths of the two rays is

ΔL = d sinθ

Slide 19

For constructive interference, d sinθ = m λ

m = 0, ±1, ±2, …

Will observe a bright fringe

The light intensity will be large

The waves will be in phase when they strike the screen

For destructive interference, d sinθ = (m + ½) λ

m = 0, ±1, ±2, …

Will observe a dark fringe

The light intensity will be zero

The waves will not be in phase when they strike the screen

Slide 20

Double-Slit Intensity Pattern

The angle θ varies as you move along the screen

Each bright fringe corresponds to a different value of m

Negative values of m indicate that the path to those points on the screen from the lower slit is shorter than the path from the upper slit

For m = 1,

Since the angle is very small, sin θ ~ θ and θ ~ λ/d

Between m = 0 and m = 1, h = W tanθ

d is the distance between the slits

W is the distance between the slits and the screen

h is the distance between the adjacent bright fringes

Slide 21

Approximations

For small angles, tan θ ~ θ and sin θ ~ θ

Using the approximations, h = W θ = W λ / d

Interference with Monochromatic Light

Light with a single frequency is called monochromatic (one color)

Light sources with a variety of wavelengths are generally not useful for double-slit interference experiments

The bright and dark fringes may overlap or the total pattern may be a “washed out” sum of bright and dark regions

No bright or dark fringes will be visible

Slide 22

Example 25 .5 Measuring the Wavelength of Light

Young’s double-slit experiment shows that light is indeed a wave and also gives a way to measure the wavelength. Suppose the double-slit experiment in Figure 25.20 is carried out with a slit spacing d=0.40 mm and the screen at a distance W=1.5 m. If the bright fringes nearest the center of the screen are separated by a distance h=1.5 mm, what is the wavelength of the light?

Solution:

Slide 23

Single-Slit Diffraction: Interference

Slits may be narrow enough to exhibit diffraction but not so narrow that they can be treated as a single point source of waves