Í þann mund sem skoðunarmaðurinn kemur, athugar hann ljósabúnaðinn.

Yes. Í þann mund sem is basically a fixed expression meaning just as, at the moment when, or right when.

So:

• Í þann mund sem skoðunarmaðurinn kemur
  = just as the inspector arrives / at the moment when the inspector arrives

This expression is a bit more formal or literary than very plain everyday wording, but it is perfectly normal Icelandic.

Good question. Normally, í can take either:

• dative for location/state: í húsinu = in the house
• accusative for movement into something: í húsið = into the house

But í þann mund is an idiomatic time expression, and it uses the accusative.

Here:

• þann = masculine accusative singular of sá
• mund = accusative singular

So even though there is no physical movement here, the phrase is simply learned as:

• í þann mund = at that moment / just then

It is best treated as a set phrase.

Here sem introduces a subordinate clause and means something like when or as.

So:

• í þann mund sem skoðunarmaðurinn kemur
  literally: at that moment that the inspector comes
• natural English: just as the inspector arrives

In Icelandic, sem is very common in relative clauses and certain time expressions like this one.

Because Icelandic very often forms nouns as compounds.

Here:

• skoðun = inspection
• maður = man/person
• skoðunarmaður = inspector / inspection officer
• skoðunarmaðurinn = the inspector

The -inn at the end is the definite article attached to the noun, so Icelandic often says the X by adding the article to the end of the word instead of using a separate word like English the.

It is the suffixed definite article, meaning the.

So:

• skoðunarmaður = an inspector
• skoðunarmaðurinn = the inspector

and

• ljósabúnaður = lighting equipment / lighting system
• ljósabúnaðinn = the lighting equipment

The exact shape of the article changes with gender, number, and case, so you will not always see just -inn, but here that is the form you get.

Yes. Icelandic often uses the present tense where English might use either a present or a future meaning, depending on context.

So kemur can mean:

• comes
• is coming
• in some contexts, will come

Likewise, the whole sentence could be understood as:

• a habitual statement:
  Whenever/just as the inspector arrives, he checks the lighting equipment
• a future-related statement:
  When the inspector arrives, he will check the lighting equipment
• a narrative present:
  Just as the inspector arrives, he checks the lighting equipment

The context tells you which reading is intended.

This is because of Icelandic V2 word order.

In main clauses, the finite verb normally comes in the second position. The first position can be taken by different elements, not just the subject.

Here, the whole subordinate clause is placed first:

• Í þann mund sem skoðunarmaðurinn kemur = first position

So in the main clause, the verb must come next:

• athugar = second position
• hann = after the verb

That is why you get:

• Í þann mund sem skoðunarmaðurinn kemur, athugar hann ljósabúnaðinn.

If the sentence started directly with the subject, you could say:

• Hann athugar ljósabúnaðinn.

But after a fronted clause, Icelandic normally inverts the order to verb + subject.

It may be obvious in meaning, but Icelandic still needs an explicit subject in the main clause.

The first part:

• sem skoðunarmaðurinn kemur

is a subordinate clause.

The second part:

• athugar hann ljósabúnaðinn

is the main clause, and it needs its own subject. Icelandic does not normally drop the subject here just because it was mentioned in the subordinate clause.

So hann = he, referring back to skoðunarmaðurinn.

It is accusative singular definite.

That is because athuga usually takes a direct object, and direct objects are commonly in the accusative.

So:

• athuga eitthvað = to check/examine something

Here the object is:

• ljósabúnaðinn = the lighting equipment

So the structure is:

• hann = subject
• athugar = verb
• ljósabúnaðinn = direct object in the accusative

It is another compound noun:

• ljós = light
• búnaður = equipment, apparatus, setup
• ljósabúnaður = lighting equipment / lighting system
• ljósabúnaðinn = the lighting equipment

The form búnað shows the accusative singular stem here, and -inn is the definite article.

So the word is long, but it is very systematic once you break it apart.

Yes: the comma separates the fronted subordinate clause from the main clause.

So the sentence is divided like this:

• Í þann mund sem skoðunarmaðurinn kemur,
• athugar hann ljósabúnaðinn.

This is similar to English punctuation in sentences like:

• When the inspector arrives, he checks the lighting equipment.

The comma helps show where the introductory clause ends.

Definitely. Depending on context, you could translate it as:

• Just as the inspector arrives, he checks the lighting equipment.
• At the moment the inspector arrives, he checks the lighting equipment.
• When the inspector arrives, he checks the lighting equipment.
• When the inspector arrives, he will check the lighting equipment.

The Icelandic sentence itself leaves some of that up to context, especially whether this is a routine action, a one-time event, or a future event.

It is understandable and normal, but it sounds a bit more elevated, written, or narrative than the most basic everyday phrasing.

A simpler everyday way might use something like:

• þegar = when

For example, a more neutral version could be:

• Þegar skoðunarmaðurinn kemur, athugar hann ljósabúnaðinn.

But í þann mund sem adds a sense of right at that moment or just as, so it is slightly more vivid and specific than plain þegar.