Az objektív a fényképezőgépen van.

Hungarian has two forms of the definite article:

• a before a consonant sound
• az before a vowel sound

So it is:

• az objektív because objektív starts with a vowel sound
• a fényképezőgépen because fényképezőgépen starts with a consonant sound

This is only a sound-based choice, like a/an in English.

The ending -en is a case ending meaning on. The full case is called the superessive case, and its forms are usually -on/-en/-ön.

So:

• fényképezőgép = camera
• fényképezőgépen = on the camera

Hungarian usually expresses ideas like on, in, to, from, etc. with endings on the noun rather than separate prepositions.

Because -ben/-ban means in, while -on/-en/-ön means on.

Compare:

• a fényképezőgépen = on the camera
• a fényképezőgépben = in the camera

A lens is understood as being attached to the outside/front of the camera, so Hungarian uses -en here, not -ben.

That is a very common point of confusion. Hungarian often omits van in the 3rd person present when the sentence identifies or describes something:

• A gép új. = The camera is new.
• Ez egy gép. = This is a machine.

But with location or existence, van is normally kept:

• Az objektív a fényképezőgépen van. = The lens is on the camera.

So here van is needed because the sentence says where something is.

In Hungarian, neutral word order often puts the most important new information before the verb, and the verb can come later than an English speaker expects.

In this sentence:

• Az objektív = topic, what we are talking about
• a fényképezőgépen = the important information about its location
• van = is

So Az objektív a fényképezőgépen van is a natural, neutral way to say The lens is on the camera.

Hungarian word order is flexible, but changes emphasis. For example:

• A fényképezőgépen van az objektív. puts more emphasis on the location.

Yes, objektív can also be the adjective objective. But in this sentence it is clearly a noun, and it means camera lens.

Context tells you which meaning is intended:

• objektív ember = an objective person
• az objektív = the lens

So here the article az and the sentence structure show that objektív is being used as a noun.

The base form is fényképezőgép, which means camera.

Then Hungarian adds the case ending:

• fényképezőgép = camera
• fényképezőgépen = on the camera

So the sentence is built very regularly: article + noun with case ending.

It is a compound word, which is very common in Hungarian.

• fényképező = photographing / photo-taking
• gép = machine

So fényképezőgép literally means something like photo-taking machine, which is the normal Hungarian word for camera.

Long words in Hungarian are often easier to understand once you identify the smaller parts.

That is just how Hungarian grammar works. The article stays separate:

• a / az = the

But case meanings such as in, on, to, from are usually expressed with suffixes attached directly to the noun:

• a házban = in the house
• az asztalon = on the table
• a fényképezőgépen = on the camera

So in Hungarian, the noun carries the location ending, not the article.

Not in the same meaning. -re means onto or to the surface of, and it usually implies movement toward that place.

Compare:

• a fényképezőgépen van = it is on the camera
• a fényképezőgépre teszem = I put it onto the camera

So for a static location, -en is correct. For motion toward the surface, -re would be used.