Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon....
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Transcript of Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon....
![Page 1: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/1.jpg)
Moon Halos.
On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle of 22 degrees) through hexagonal ice crystals in the atmosphere. The mathematics is as follows:
![Page 2: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/2.jpg)
Hexagonal ice crystals look something like this.
![Page 3: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/3.jpg)
A side-on view of an ice crystal
![Page 4: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/4.jpg)
When light strikes the boundary between two different substances (air and ice) it refracts.
Air-Ice boundary
Light ray
![Page 5: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/5.jpg)
Snell’s Law is the physical relation governing refraction. It states that the angle of incidence and the angle of refraction are related by the formula
.sin
sin
2
1 k
The constant k depends on the nature of the two substances. For air-ice, it is about 1.31.
![Page 6: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/6.jpg)
Light enters the crystal, and then leaves it, making two refractions.
θ1
θ2
θ3
θ4
![Page 7: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/7.jpg)
Here, the angle α represents the total angle the light bends.
θ1
θ2
θ3
θ4
![Page 8: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/8.jpg)
The necessary relations needed to determine α are on the next slide.
![Page 9: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/9.jpg)
θ1
θ2
θ3
θ4
180180
,180120,sin
sin,
sin
sin
3421
323
4
2
1
kk
![Page 10: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/10.jpg)
We solve the relations on the next slide.
180180
,180120,sin
sin,
sin
sin
3421
323
4
2
1
kk
![Page 11: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/11.jpg)
11221
1
1111
1
1111
41
31
4
23
112
sinsin32
1sin60
sin2
1sinsincos
2
3sin60
sinsin60sinsin60
60
sinsin
60
sinsin
k
kk
kk
k
k
![Page 12: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/12.jpg)
11221
1 sinsin32
1sin60 k
“Technically speaking”, there are about a zillion ice crystals in the atmosphere all oriented randomly. The angle
1
will take many different values.
![Page 13: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/13.jpg)
11221
1 sinsin32
1sin60 k
This means that the light will be scattered through many different angles, though there is a catch.
![Page 14: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/14.jpg)
11221
1 sinsin32
1sin60 k
If there are many different angles of incidence
1
that yield approximately the same α, light will seem to build up at that angle.
![Page 15: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/15.jpg)
Light builds up most where the slope is smallest. This is 21.83929990 degrees.
![Page 16: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/16.jpg)
This is the classic 22˚ moon halo.
22˚
Diffuse clouds
Apparent Halo
Moonlight
![Page 17: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/17.jpg)
Light inside the halo is refracted out in a cone that misses the observer, making this region less bright to the observer.
Diffuse clouds
Apparent Halo
Moonlight
![Page 18: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/18.jpg)
Light outside the halo is refracted out in a cone that misses the observer, making this region less bright to the observer.
Diffuse clouds
Apparent Halo
Moonlight
![Page 19: Moon Halos. On nights with diffuse high clouds and a bright moon, a halo can appear about the moon. This results from light refracting (through an angle.](https://reader035.fdocuments.net/reader035/viewer/2022081822/5697bfe81a28abf838cb6615/html5/thumbnails/19.jpg)
Light on the halo is refracted out in a cone that the observer sees, making this region brighter to the observer.
Diffuse clouds
Apparent Halo
Moonlight