The Brocken Spectre and Green Flash
The phenomenon of Brocken Spectre and Green Flash can be observed not only at high mountain, but also at level ground.
 Links The Brocken Spectre # Brocken For more photographs Travel note of Mt. Brocken Scientific explanation How-to watch it How-to take a picture # Atmospheric Optics # Green Flash # Mysterious Flying Object This photograph is a Brocken Spectre(glory,halo) appeared in the mist near the ridge of Mt.Hotaka in Japan. For more sample of photograph, click here. This phenomenon of Brocken Spectre looks like a rainbow, but its principle differs. Its radius angle is about  3 or 4 degrees (rainbow is 42 degrees). It has number of rings, sometimes comes up to 3 or more. It appears in a mist and cloud (rainbow appears in a rain). For more Scientific explanation, click here. In Japan, old Buddhist believed it as an appearance of the Amitabha. The name originates from the Mt.Brocken (1,142m) in Germany. This is a travel note of Mt.Brocken.

# How-to experience the Phenomenon of Brocken Spectre

(1)The condition of phenomenon
The sunbeams comes from backward, and illuminates the cloud or mist directly in front of you, and your shadow lay on it.

(2)in the mountains
To secure the view and direct sunbeam, the top or ridge of high mountain is suitable.
The cloud or mist is required, but rough weather prevents the direct sunbeam. Therefore, you can make likelihood strong choosing the timing near sunrise or sunset in the fine days. These timing often have cloud or mist even in a fine day.

Almost all photographs in my page are taken in the timing of sunrise or sunset, in a fine day of mountain up to 2,500m.

(3)at low land or airplane or under experimental condition
In Tadami-town Fukusima-pref. Japan, it can be watched on the surface of the stream in early summer. This is because the cool water from thawing of high mountain makes fog on the stream, and people easily watch down it from bridges in a fine day.

I confirmed it appears in the mist from liquid nitrogen under the sunlight. You can also try it with dry ice.

From aircraft, it can be watched on the low cloud. But in a high cloud, it does not appear. This is because high cloud consists from crystal of ice, not from round water particle.

#
How-to
take a photograph

(1)Exposure
In case of single lens reflex camera and expecting the best result, adjust the exposure value to the brocken phenomenon. This exposure seems little bit dark, but it is the best condition. Never make it light, not to make it white and not to lose the information of image.

In case of simple camera, leave it to the camera. Many negative films may record a wide range of light.

(2)Focus
Focus on the object near the phenomenon. Brocken phenomenon do not have clear edge, we do not need a fine focusing.

# The principle of Brocken Spectre

Brocken Spectre is a kind of Mie scattering. Following table shows the relation between particle in the air and scattering.
 size of particle mechanism of scattering smaller enough than the wavelength of light << Rayleigh Scattering >> Particle scatters short(blue) light wave to every direction. The color of blue sky is atmospheric Rayleigh scattering. near the wavelength of light << Mie Scattering >> This scattering contains many effect such as diffraction, interference, resonance (multiple reflection) and surface wave. Mie scattering has some peaks in the backward, as the result, we can watch some rings in the Brocken phenomenon. larger enough than the wavelength of light << Refraction and Reflection >> The sunbeam refracted and reflected in the raindrops makes the Rainbow.

Mie scattering is very complicated and cannot explained simply. But I tried to simulate it very simply. Following graph is a calculation of disc backscattering (substitute of spherical water particle) .
I think that this is not correct enough, but it shows some characteristics having a dot of light in the center, and the order of color is blue, green, red, and the smaller the particle comes, the wider the interval of rings become.

This calculation is based on following complex integration.
$\left\{\int \right\}_\left\{0\right\}^\left\{r\right\} \left\{\int \right\}_\left\{0\right\}^\left\{2\pi \right\}\left\left(\exp\left\left(\left\{i\frac\left\{2\pi \right\}\left\{\lambda \right\}\right\}\right\right)×L×sin\theta ×cos\phi \right\right)L \phi L$
However, this model results a kind of 'sinc function' which has its maximum peak at front angle, and not exact approximation. I tried using many plane representing the sphere in vain.
The fact I could confirmed was that larger the sphere becomes, smaller the ring becomes.

Following image is calculated based on the next URL, adding fog to adjust it with what I saw.

The relation between the size of scattering particle and brocken ring size can be confirmed using laser beam as following movie.

In the following photograph , the ring of light is not concentric. This is considered that the size of scattering particle differs spot by spot.

 Atmospheric Optics Circumhorizontal arc Hexagonal crystal of ice refracts the sun beam with 46 degree.  This phenomenon can be observed when the sun is higher than 46 degree. The direction of each ice is almost the same and lies flat because of their  slow falling speed. High-Resolution for another picture Circumzenthal arc This is almost same as Circumhorizontal arc, but the route is different. Sun pillar The base of hexagonal crystal of ice reflects the sun beam . Halo Long hexagonal ice, like a pencil, refracts the sun beam. for more picture Tangent arc (on the above of picture, not around the sun) Same with Halo, but when the arc becomes long, the shape becomes 'U'. Parhelion This one's principle is the same with Halo, but the direction of each ice is almost the same and lies flat, because of their slow falling speed.. for more picture Rainbow We can find more than 3 rainbows at the same time. One is usual rainbow, and the second one is called Secondary rainbow outside of the primary one. The band between the primary rainbow and the secondary one is called the Dark Alexander  Band. The third rainbow inscribes the primary one. This is a result of interference between light waves. a comparison of size between rainbow and brocken phenomenon (calcuration) Copyright Since 1999 by KOCK, All Rights Reserved.

 The Green Flash It was Mt.Shirouma in Japan where I found that the green light flashed just before the sun set completely. This photograph shows the sunrise with green shimmer, which produced by the flicker of the atmosphere. I think this is related to the green flash. The sunbeam is refracted by the atmosphere, and only green light can reach to us just before the sun set. Blue ray is in the view, but the Rayleigh scattering prevents its reach. Why dose it flash ? I think the flicker of atmosphere sometime make it flash and we cannot experience it every time.

 other phenomenon It was the first experience for me that I had fond  these kind of object flying like a balloon. Click to play YouTube video --> Comparing with antenna elements, the size of this object is estimated about at least 1.0m when the distance of this object was 200m (distance is eye measurement and assumption). 9/July/2008,18:04 JST Yokohama,Japan Original still image : photo#1 , photo#2 , photo#3