Το ουράνιο τόξο εμφανίζεται μετά τη βροχή.

Το is the definite article meaning the for a neuter singular noun.

Here, the main noun is τόξο (rainbow is the fixed expression ουράνιο τόξο), and that expression is neuter singular, so the article is το.

• το = the for neuter singular nouns
• ουράνιο τόξο = rainbow

So Το ουράνιο τόξο = the rainbow.

In Greek, rainbow is commonly expressed as ουράνιο τόξο, literally something like heavenly/sky bow.

• ουράνιο = heavenly / celestial / sky-related
• τόξο = bow

Together they form a set expression meaning rainbow.

This is very normal in Greek: sometimes one English word corresponds to a multi-word expression in Greek.

Because ουράνιο is an adjective, and it has to agree with τόξο.

• τόξο is neuter singular
• so the adjective also has to be neuter singular
• that gives ουράνιο

Compare:

• ουράνιος = masculine form
• ουράνια = feminine form
• ουράνιο = neuter form

Since τόξο is neuter, Greek uses ουράνιο τόξο.

εμφανίζεται means appears, shows up, or becomes visible.

It comes from the verb εμφανίζομαι, which is often used in the sense of to appear.

In this sentence:

• Το ουράνιο τόξο εμφανίζεται = The rainbow appears

It is a very natural verb here because a rainbow is something that becomes visible rather than something that actively "does" an action.

Great question. εμφανίζεται has a middle/passive-style ending (-εται), but here it is best translated actively as appears.

Greek has verbs that use these endings even when English does not use a passive translation. So although the form looks passive to learners, in many cases it functions more like:

• it appears
• it shows up

So in this sentence, εμφανίζεται does not mean is being appeared. It simply means appears.

It is present tense, third person singular.

So literally it is:

• it appears

Greek often uses the present tense for:

• general truths
• habitual events
• descriptions of what typically happens

That is exactly what is happening here: the sentence describes what usually happens after rain.

Here μετά means after, and when μετά is used in modern Greek to mean after, it is followed by the accusative.

So:

• η βροχή = the rain (nominative)
• τη βροχή = the rain (accusative)

That is why the sentence says:

• μετά τη βροχή = after the rain

Both are connected to the same article: την.

In modern Greek, the final -ν in την is sometimes dropped before certain consonants, especially in everyday writing and speech. That is why you often see:

• τη βροχή

instead of

• την βροχή

Because β is one of the consonants before which dropping the -ν is common, τη βροχή is perfectly normal.

So:

• τη βροχή and την βροχή both mean the same thing here
• τη βροχή is the more usual form in this context

Greek often uses the definite article where English may or may not use one.

So Greek prefers:

• μετά τη βροχή = literally after the rain

Even when English might say:

• after rain
• after the rain
• after it rains

Greek commonly keeps the article with nouns in expressions like this. So μετά τη βροχή sounds natural and standard.

Yes. Greek word order is more flexible than English word order.

The neutral, straightforward order here is:

• Το ουράνιο τόξο εμφανίζεται μετά τη βροχή.

But other orders are possible, depending on emphasis, for example:

• Μετά τη βροχή εμφανίζεται το ουράνιο τόξο.
• Μετά τη βροχή, το ουράνιο τόξο εμφανίζεται.

These all mean roughly the same thing, but the emphasis shifts slightly:

• putting μετά τη βροχή first highlights when it happens

Still, the original version is very natural and easy for learners.

A rough pronunciation guide is:

To ouránio tóxo emfanízetai metá ti vrohí.

A few helpful notes:

• ου sounds like oo in food
• χ in τόξο and βροχή is the Greek kh/h sound, not an English k
• β in modern Greek sounds like v, not like English b
• the stressed syllables are:
  • ouránio
  • tóxo
  • emfanízetai
  • metá
  • vrochí

Yes, βροχή is feminine.

You can tell from the dictionary form:

• η βροχή = the rain

The article η marks it as feminine in the nominative singular.

Then in the accusative singular it becomes:

• τη(ν) βροχή

So in this sentence:

• η βροχή → base form
• τη βροχή → the form used after μετά

Not usually in this sentence.

• έρχεται means comes
• εμφανίζεται means appears / becomes visible

For a rainbow, εμφανίζεται is much more natural, because a rainbow is something that appears in the sky, not something that literally comes somewhere.

So:

• Το ουράνιο τόξο εμφανίζεται μετά τη βροχή. = natural
• Το ουράνιο τόξο έρχεται μετά τη βροχή. = unnatural in most contexts

Normally, it is understood as a general fact or typical occurrence:

• The rainbow appears after the rain

Greek present tense often works this way, just like English present tense in sentences such as:

• Water boils at 100°C
• The sun rises in the east

So the sentence is not necessarily saying the rainbow is appearing right now. It is more naturally understood as this is what happens after rain.