Wave Optics

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Solution:

Slide 29

Optical Resolution and the Rayleigh Criterion

For a circular opening of diameter D, the angle between the central bright maximum and the first minimum is

The circular geometry leads to the additional numerical factor of 1.22

Slide 30

Rayleigh Criterion

If the two sources are sufficiently far apart, they can be seen as two separate diffraction spots (A)

If the sources are too close together, their diffraction spots will overlap so much that they appear as a single spot (C)

A B C

Two sources will be resolved as two distinct sources of light if their angular separation is greater than the angular spread of a single diffraction spot.

Slide 31

This result is called the Rayleigh criterion

For a circular opening, the Rayleigh criterion for the angular resolution is

Two objects will be resolved when viewed through an opening of diameter D if the light rays from the two objects are separated by an angle at least as large as θmin

Slide 32

Example 25 .7 Rayleigh Criterion for a Marksman

A rifle used for target shooting has a small telescope so that the shooter can accurately aim at his target. Suppose the telescope has a diameter D=1.5 cm and the shooter is looking at two small objects that are L=200 m away. If the shooter is just barely able to tell that there are two objects (and not one), how far apart are the objects? Assume red light with λ=600 nm.

Solution:

Slide 33

Why Is the Sky Blue?

The light we see from the sky is sunlight scattered by the molecules in the atmosphere

The molecules are much smaller than the wavelength of visible light

They scatter blue light more strongly than red

This gives the atmosphere its blue color

Blue sky

Although violet scatters more than blue, the sky appears blue

The Sun emits more strongly in blue than violet

Our eyes are more sensitive to blue

The sky appears blue even though the violet light is scattered more

Sun near horizon

There are more molecules to scatter the light

Most of the blue is scattered away, leaving the red