Όταν βγαίνει το ουράνιο τόξο, η ανιψιά μου χαμογελάει.

In Greek, όταν often introduces a repeated or general situation, so the present tense is very natural.

So Όταν βγαίνει το ουράνιο τόξο, η ανιψιά μου χαμογελάει means something like:

• Whenever the rainbow appears, my niece smiles
• or When the rainbow comes out, my niece smiles

Greek uses the present here for a habitual or general idea, just like English can use the present in when clauses.

Βγαίνει comes from βγαίνω, which literally means to go out, to come out, or to emerge.

For things like the sun, moon, stars, or a rainbow, Greek often uses βγαίνω to mean appear or come out.

So:

• βγαίνει το ουράνιο τόξο = the rainbow appears / comes out

This is a very natural Greek way to say it, even if English more often says the rainbow appears.

Το ουράνιο τόξο means the rainbow.

Literally, it is made up of:

• ουράνιο = heavenly, celestial, or of the sky
• τόξο = bow

So the literal sense is something like the heavenly bow or sky bow.

It is a fixed expression in Greek for rainbow.

Greek uses the definite article much more often than English does.

So where English might say:

• When a rainbow appears
• or When the rainbow appears

Greek very naturally says:

• Όταν βγαίνει το ουράνιο τόξο

Using το here does not necessarily mean one specific rainbow. It often just sounds like the normal way to talk about the phenomenon in general.

The same is true for η ανιψιά μου: Greek usually keeps the article with family words and many nouns.

Both are possible in some contexts, but η ανιψιά μου is the most standard full form.

Greek very often uses the definite article with possessive expressions:

• η ανιψιά μου = my niece
• ο αδερφός μου = my brother
• το σπίτι μου = my house

So even though English does not say the my niece, Greek naturally does.

Ανιψιά means niece.

Related forms are:

• ο ανιψιός = nephew
• η ανιψιά = niece

So in this sentence, the speaker is specifically talking about a female niece.

In Greek, possessive words like μου usually come after the noun:

• η ανιψιά μου = my niece
• το βιβλίο μου = my book

This is the normal Greek pattern.

So while English says my niece, Greek says something more like the niece of me in structure.

Yes. Both χαμογελάει and χαμογελά are correct.

They are two common present-tense forms of χαμογελώ / χαμογελάω:

• χαμογελάει
• χαμογελά

Both mean he/she smiles.

The longer form χαμογελάει is very common in everyday speech and writing. The shorter form χαμογελά is also standard.

So you could also say:

• Όταν βγαίνει το ουράνιο τόξο, η ανιψιά μου χαμογελά.

Normally, it sounds like a repeated or habitual action.

So the idea is:

• Whenever the rainbow appears, my niece smiles

If you wanted to make it clearly about one specific moment, the context would usually show that. But with όταν + present and present in the main clause, the default feeling is often general/habitual.

The sentence begins with a time clause:

• Όταν βγαίνει το ουράνιο τόξο = When the rainbow appears

Then comes the main clause:

• η ανιψιά μου χαμογελάει = my niece smiles

Greek commonly uses a comma when a subordinate clause comes first, just as English often does:

• When the rainbow appears, my niece smiles.

So the comma here is completely normal.

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

For example, you could also say:

• Η ανιψιά μου χαμογελάει όταν βγαίνει το ουράνιο τόξο.

This means the same thing.

The version with όταν first slightly foregrounds the time condition: When the rainbow appears...

Greek can also shift word order for emphasis, but the original sentence is very natural and neutral.

Because in Greek, the subject is explicitly stated as το ουράνιο τόξο.

English might say:

• when the rainbow appears
• or when it comes out

Greek simply says:

• όταν βγαίνει το ουράνιο τόξο

There is no need for an extra it, because the rainbow is already the subject of the verb βγαίνει.

Also, Greek generally does not use an empty subject like English sometimes does.

A simple pronunciation guide would be:

• Όταν ≈ OH-tan
• βγαίνει ≈ VYEH-ni
• το ουράνιο τόξο ≈ to oo-RA-nee-o TOK-so
• η ανιψιά μου ≈ ee a-nip-SYA moo
• χαμογελάει ≈ ha-mo-ge-LA-ee

A few useful notes:

• αι is usually pronounced like e
• ει is also pronounced like ee
• the stress matters a lot in Greek, so pay attention to the accented syllables:
  • Όταν
  • βγαίνει
  • ουράνιο
  • τόξο
  • ανιψιά
  • χαμογελάει