Atmospheric Optics - II

RECAP•Human perception of color, white objects, black objects.

•Light scattering: light is sent in all directions –forward, sideways and backward♦ Geometric scattering: R>>(all wavelengths equally scattered) ♦ Mie scattering: R~(red is scattered more efficiently)♦ Rayleigh scattering: R<<(blue is scattered more efficiently)

•Phenomena: white clouds, blue skies, hazy skies, crepuscular rays, colorful sunsets, blue moon.

•Refraction: the bending of the light ray as it travels from one medium to another. It bends towards the vertical if it enters a more-dense medium and away from the vertical as it enters a less-dense medium. ♦ Phenomena: stars appear higher in the sky, twinkling, twilight.

•Reflection: the angle of incidence is equal to the angle of reflection

•Total internal reflection: mirages

•Dispersion: separation of colors when light travels through a medium.♦ rainbow

TODAY:

Reflection and Refraction of Light

•The speed of light in vacuum is c=300,000 km/s

•Snell’s law: The angle of incidence is equal to the angle of reflection.

•Light that enters a more-dense medium slows down and bends toward the normal.

•Light that exits a more-dense medium speeds up and bends away from the normal.

True and apparent position of objects

•Due to the refraction of light the objects on the sky appear higher than they actually are.♦ Star location and scintillations;

♦ Timing of the sunset and the sunrise;

♦ The sun on the horizon looks flattened;

♦ Twilight.

The Timing of the Sunset & Sunrise

We see the sun before it actually rises above the horizon and after it sets below the horizon.

Twilight

Flattening of the Sun’s Disk at Sunset

Green flash

Flattening of the MoonRefraction by the Earth’s atmosphere (image from ISS)

http://www.sundog.clara.co.uk/atoptics/phenom.htm

Total Internal Reflection

air

water

water

water

air air

Total internal reflection (dense->less dense)

Refraction (dense->less dense)

Refraction (less dense->dense)

Cold air

Hot air

•The light travels from more dense towards less dense medium.

•If the incident angle exceeds the critical angle the light is fully reflected.

cr

cr

Mirages

•Description: an object is displaced from its true position.

•Physical process: the light form the object is strongly refracted due to changes of the atmospheric density.

•Classification:♦ Inferior: pool on the road, oasis in the desert♦ Superior: mountains and castles on the sea horizon

Thin layer of hot, less-dense air

•Conditions for an inferior (inverted) mirage

•Conditions for a superior (upright) mirage

Fata Morgana (a.k.a.Morgan le Fay)

•Objects on the horizon, such as islands, cliffs, ships or icebergs, appear elongated and elevated, like "fairy tale castles".

•It is frequently seen where warm air rests over a cold surface, such as above large bodies of water and in polar regions

A Fata Morgana seen on the Norwegian coast

A desert mirage A highway mirage

Sunset mirageSuperior mirage: a layer of abnormally warm air above cooler air.

http://www.sundog.clara.co.uk/atoptics/phenom.htm

Etruscan Vase Sunset Mirage•As the sun sinks a second sun appears to rise from the water.

 The two eventually join at a thin red colored stem.  

•The lower sun is not a reflection from the water. It is an inferior mirage. The lower sun, an inverted image of the upper one, is produced by refraction in a lower layer of warm and less dense air.  

http://www.sundog.clara.co.uk/atoptics/phenom.htm

Sunset mirage (pancake suns)

Here the atmosphere's vertical temperature profile is complex. There are at least three layers with different temperatures and the central layer is possibly cooler than those above and below it. Each pancake is an image of a particular slice through the sun.

http://www.sundog.clara.co.uk/atoptics/phenom.htm

Optical Effects from Ice Crystals

22 deg Sun Halo

• It is caused by randomly oriented ice crystals with a shape of hexagonal prism.

• The crystals whose axes are roughly perpendicular to the direction of sunlight refract its rays through 22º or more. Each sparkles in the sky when it is at this angular distance from the sun. The collective sparkles form the halo.

Sun Dogs

Dispersion

Tangent Arcs

•The long axes of the ice crystals are horizontal to the ground.

Sun pillars

•Reflection from plate-like ice crystals that are horizontally oriented and wobble as they fall

Optical effects from water dropletsRainbow

Secondary Bow

Primary Bow

Alexander’s dark band

Bright sky inside the bow

Rainbows are caused by internal reflection of solar light by raindrops.

Rainbow Viewing Geometry

•The observer is between the sun and the rainbow.

•The rainbow angle is 42.5 degrees.

Creating a Rainbow

•The primary rainbow is caused by a single internal reflection from the raindrop.

•The secondary rainbow is the result of a double internal reflection from the surface of the raindrop.

•The color separation is due to dispersion of light in the process of refraction.

•The red color is on the outside of

the primary and on the inside of

the secondary bow.

in

out

Summary

•Mirages are caused by atmospheric layers with different densities:♦ Inferior (e.g. wet road): cold air over hot air♦ Superior (e.g. Fata Morgana): hot air over cold air

•Water droplets cause:♦ Rainbows

•Primary

•Secondary (2 internal reflections)

•Ice crystals cause:♦ Sundogs♦ Halos♦ Tangents♦ Sun pillars