هذا فحص نظر.

Because Arabic normally omits the present-tense verb "to be" in simple sentences like this.

So:

• هذا فحص نظر = This is an eye exam

Literally, it looks more like:

• this eye-exam

But grammatically, Arabic understands it as a complete sentence.

If you wanted past or future, Arabic would use a verb such as كان:

• كان هذا فحصَ نظرٍ = This was an eye exam

Because فحص is a masculine singular noun, and هذا is the masculine singular word for this.

• هذا = this (masculine)
• هذه = this (feminine)

So if the main noun were feminine, you would use هذه instead.

Yes. فحص نظر is a single noun phrase built as an iḍāfa (construct phrase).

It is literally:

• فحص = examination / test
• نظر = vision / sight / eyesight

So together it means:

• an eye exam
• literally an examination of vision

In grammar terms:

• فحص = the first part of the iḍāfa
• نظر = the second part, which tells us what kind of examination it is

This is because of how iḍāfa works.

In an iḍāfa:

• the first noun normally does not take ال
• the whole phrase’s definiteness is mainly determined by the second noun

So here:

• فحص نظر = an eye exam / a vision test
  The phrase is indefinite

If you made the second noun definite:

• فحصُ النظرِ

then the whole phrase becomes definite, roughly:

• the eye exam
• the vision exam
• the examination of eyesight

Good question. In this sentence, هذا is being used as the subject of a full sentence, and فحص نظر is the predicate.

So the structure is:

• هذا = this
• فحص نظر = an eye exam

Together:

• This is an eye exam

If Arabic wanted a phrase meaning this eye exam as one noun phrase rather than a full sentence, it would usually be expressed differently, often with a definite structure or a different placement of the demonstrative.

So in this exact form, learners should usually read it as a complete sentence.

Here, نظر is a noun, not a verb.

Depending on context, نظر can be related to:

• looking
• sight
• vision
• eyesight

In a medical phrase like فحص نظر, it means vision / eyesight.

So this is not he looked or anything verbal here. It is part of the noun phrase eye exam.

In fully vocalized Modern Standard Arabic, it would be:

• هٰذا فَحْصُ نَظَرٍ

Here is what is happening:

• فحصُ is nominative because it is the predicate of the sentence
• نظرٍ is genitive because it is the second word in the iḍāfa
• فحص does not take tanwīn because the first noun in an iḍāfa does not take it

In normal Arabic writing, these short vowels are usually left out, so you just see:

• هذا فحص نظر

A careful pronunciation with case endings is:

• hādhā faḥṣu naẓarin

In normal everyday reading, without emphasizing endings, learners often say something closer to:

• hādhā faḥṣ naẓar

A few sound notes:

• ح in فحص is a deeper, breathier h than English h
• ظ in نظر is an emphatic sound, often approximated for learners as a heavy z

So this sentence is short, but it contains two sounds that English speakers often need to practice.