Büyüteç masanın altında bulundu.

Because Turkish usually uses the genitive + possessed form pattern with words like üst (top), alt (bottom/under), iç (inside), ön (front), and arka (back).

So:

• masa = table
• masanın = of the table / the table’s
• altı = its underside / the area under it
• masanın altı = the underside of the table / the area under the table

Then the locative ending is added:

• masanın altında = under the table

So masanın is required because altında is part of a possessed structure, not just a simple postposition.

Altında can be broken down like this:

• alt = lower part, underside, below
• -ı = third-person possessive ending (its)
• -nda = locative ending (in/on/at), appearing here as -nda

So:

• altı = its lower part / underneath it
• altında = in/at its lower part, which naturally means under it

With masanın before it, the whole phrase becomes:

• masanın altında = under the table

This is a very common Turkish pattern.

Because bulundu and buldu are different verbs/forms.

• buldu = he/she/it found
• bulundu = was found or was located

Here, bulundu comes from bulunmak.

Depending on context, bulunmak can mean:

• to be found
• to be located
• to exist / be present

So in this sentence, Büyüteç masanın altında bulundu most naturally means:

• The magnifying glass was found under the table or, in some contexts,
• The magnifying glass was located under the table

If the sentence were Büyüteci masanın altında buldu, that would mean He/she found the magnifying glass under the table.

It is in the simple past (also called the definite past) in Turkish.

The ending -du shows a completed action or situation in the past:

• bulun-du = was found / was located

This tense is typically used for something the speaker presents as a definite fact.

The subject is büyüteç.

• büyüteç = magnifying glass

It has no accusative ending, so it is not a direct object here. It is the thing being talked about, and the verb agrees with it in meaning as the thing that was found or was located.

So the basic structure is:

• Büyüteç = subject
• masanın altında = location
• bulundu = verb

Turkish does not have articles like English a/an and the.

So büyüteç can mean:

• a magnifying glass
• the magnifying glass

The exact meaning depends on context.

Likewise:

• masa can mean a table or the table

In this sentence, English often uses the because the context usually makes the noun specific:

• The magnifying glass was found under the table.

Most directly, bulundu suggests:

• was found or
• was located

It does not usually mean a simple static was in the same way as English was under the table.

If you only want to say where something was, Turkish often uses other structures, for example with vardı in past contexts:

• Büyüteç masanın altındaydı. = The magnifying glass was under the table.

So bulundu usually adds the idea of being discovered or being situated/found there.

A very normal Turkish word order is:

• Subject + place/time + verb

So:

• Büyüteç = subject
• masanın altında = place
• bulundu = verb

This is completely natural Turkish.

Turkish word order is flexible, though, and parts can be moved for emphasis. For example, a speaker might change the order to emphasize the location. But the version you have is a standard, neutral sentence.

There are two important case-related forms here:

1. masanın

   • root: masa
   • ending: -ın
   • function: genitive
   • meaning: of the table / the table’s

2. altında

   • based on altı
   • ending: -nda
   • function: locative
   • meaning: at/in its lower part, so under it

So the phrase uses the common Turkish pattern:

• [noun in genitive] + [location word with possessive + locative]

That is why under the table is not built as a single preposition, but as a small structure.

Yes, büyüteç is the standard word for magnifying glass.

It comes from the idea of making something bigger/magnified:

• büyü- relates to growing or becoming bigger
• -teç is a noun-forming element in some words for instruments or devices

You do not need to analyze it every time, though. It is best learned as a whole vocabulary item:

• büyüteç = magnifying glass

Not in standard Turkish for this meaning.

To say under the table, you normally need:

• masanın altında

This is because alt behaves like a relational noun, and it typically requires the genitive-possessive pattern.

So:

• masanın altında = correct
• masa altında = generally not the normal way to say under the table

The full structure is the standard one learners should use.