Parhelic circle

Key takeaways

Parhelic circle belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Parhelic circle to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Parhelic circle from memory before moving on to harder problems.

Reference excerpt

A parhelic circle is a type of halo, an optical phenomenon appearing as a horizontal white line on the same altitude as the Sun, or occasionally the Moon. If complete, it stretches all around the sky, but more commonly it only appears in sections. If the halo occurs due to light from the Moon rather than the Sun, it is known as a paraselenic circle. Even fractions of parhelic circles are less common than sun dogs and 22° halos. While parhelic circles are generally white in colour because they are produced by reflection, they can however show a bluish or greenish tone near the 120° parhelia and be reddish or deep violet along the fringes. Parhelic circles form as beams of sunlight are reflected by vertical or almost vertical hexagonal ice crystals. The reflection can be either external (e.g. without the light passing through the crystal) which contributes to the parhelic circle near the Sun, or internal (one or more reflections inside the crystal) which creates much of the circle away from the Sun. Because an increasing number of reflections makes refraction asymmetric some colour separation occurs away from the Sun. Sun dogs are always aligned to the parhelic circle (but not always to the 22° halo). The intensity distribution of the parhelic circle is largely dominated by 1-3-2 and 1-3-8-2 rays (cf. the nomenclature by W. Tape, i.e. 1 denotes the top hexagonal face, 2 the bottom face, and 3-8 enumerate the side faces in counter-clockwise fashion. A ray is notated by the sequence in which it encounters the prism faces). The former ray-path is responsible for the blue spot halo which occurs at an azimuth.

θ 1 3 2 = 2 arcsin ⁡ ( n cos ⁡ ( arcsin ⁡ ( 1 / n ) ) / cos ⁡ ( e ) ) {\displaystyle \theta _{{\mathfrak {1}}{\mathfrak {3}}{\mathfrak {2}}}=2\arcsin \left(n\cos \left(\arcsin \left(1/n\right)\right)/\cos \left(e\right)\right)} , with n {\displaystyle n} being the material's index of refraction (not the Bravais index of refraction for inclined rays). However, many more features give a structure to the intensity pattern of the parhelic circle. Among the features of the parhelic circle are the Liljequist parhelia, the 90° parhelia (likely unobservable), the second order 90° parhelia (unobservable), the 22° parhelia and more. Artificial parhelic circles can be realized by experimental means using, for instance, spinning crystals.

See also Upper and lower tangent arcs Circumzenithal arc Liljequist parhelion

References

External links Atmospheric Optics – Ice Halos

Illustrations

Worked examples

Example 1 — a first encounter with Parhelic circle

Start with the simplest possible case. Write down what Parhelic circle claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Parhelic circle before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Parhelic circle ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Parhelic circle

In research: Parhelic circle appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Parhelic circle in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Parhelic circle is common in secondary-school and first-year university syllabi. It links to neighbouring topics Atmospheric optical phenomena, so understanding it makes those chapters shorter.
In everyday life: Look for Parhelic circle outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Parhelic circle in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Parhelic circle means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Parhelic circle out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Parhelic circle in simple terms?

A parhelic circle is a type of halo, an optical phenomenon appearing as a horizontal white line on the same altitude as the Sun, or occasionally the Moon. If complete, it stretches all around the sky, but more commonly it only appears in sections.

Why does Parhelic circle matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Parhelic circle?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Parhelic circle.