Az optometrista a látóteret és a szemfeneket ellenőrzi.

Hungarian has one definite article, but it has two forms:

• a before a consonant
• az before a vowel

So:

• az optometrista because optometrista starts with a vowel
• a látóteret
• a szemfeneket because those start with consonants

This is purely a sound-based choice, like making the sentence flow more smoothly.

They are the direct objects of the verb, so they take the accusative ending.

The basic nouns are:

• látótér = visual field
• szemfenék = fundus / back of the eye

As direct objects, they become:

• látóteret
• szemfeneket

The important accusative marker is really -t. The extra e is a linking vowel that makes pronunciation easier.

Also notice that the long vowel in the last syllable shortens before the ending:

• tér → teret
• fenék → feneket

That kind of stem change is very common in Hungarian.

Because Hungarian uses two kinds of verb conjugation:

• indefinite conjugation
• definite conjugation

Here the objects are definite: a látóteret and a szemfeneket both mean the visual field and the fundus, so Hungarian uses the definite verb form:

• ellenőrzi = he/she checks it / the specific thing

Compare:

• ellenőriz = he/she checks, is checking something
• ellenőrzi = he/she checks it / the specific object

Since the sentence has definite objects, ellenőrzi is the correct choice.

The dictionary form is ellenőriz, and the infinitive is ellenőrizni.

In this sentence:

• ellenőrzi = present tense
• 3rd person singular
• definite conjugation

So it means he/she checks or is checking with a definite object.

Hungarian word order is much more flexible than English word order. It often depends on topic and focus, not just grammar.

In this sentence:

• Az optometrista is the topic, what the sentence is about
• a látóteret és a szemfeneket comes before the verb
• ellenőrzi comes at the end

This is a very natural Hungarian sentence pattern.

You could also say:

• Az optometrista ellenőrzi a látóteret és a szemfeneket.

That is also grammatical, but it sounds a little different in emphasis and rhythm. Hungarian word order often reflects what is being highlighted.

És means and.

It joins the two objects:

• a látóteret
• a szemfeneket

So both things are being checked.

In Hungarian, when two definite nouns are joined with és, it is very normal to repeat the article before each one.

So:

• a látóteret és a szemfeneket

This is the most natural standard phrasing here.

English often avoids repetition more easily, but Hungarian commonly keeps the article with each coordinated noun.

Yes, both are compounds.

• látótér = látó
  • tér
    • látó relates to seeing
    • tér means space/area/field

So the literal idea is something like field of seeing.

• szemfenék = szem
  • fenék
    • szem = eye
    • fenék = bottom/base

So the literal idea is the bottom/back of the eye, which matches the medical meaning.

Hungarian uses compounds very often, especially in technical and medical vocabulary.

Az optometrista is the subject of the sentence.

It is in the basic form, with no special ending, because subjects in Hungarian are normally unmarked in the nominative.

So the structure is:

• Az optometrista = subject
• a látóteret és a szemfeneket = direct objects
• ellenőrzi = verb

A few useful points:

• Hungarian stress is almost always on the first syllable of the word.
• Accents usually mark vowel length, not stress.

For example:

• optometrista → stress on op
• látóteret → stress on lá
• szemfeneket → stress on szem
• ellenőrzi → stress on el

Some vowel notes:

• á is a long vowel
• é is a long vowel
• ő is a long rounded vowel, a sound English does not really have

So in ellenőrzi, the ő is important and should be kept long.

Yes, very often Hungarian can leave out the subject if it is clear from context, because the verb form already shows person and number.

So in context, someone could say just:

• A látóteret és a szemfeneket ellenőrzi.

That would mean something like He/She is checking the visual field and the fundus.

But in your sentence, Az optometrista is included because the speaker wants to state clearly who is doing the checking.