Þokan varð svo þykk við ströndina að við biðum í bílnum í smástund.

Þoka means fog. Þokan means the fog.

Icelandic usually puts the definite article on the end of the noun instead of using a separate word like English the. So here:

• þoka = fog
• þokan = the fog

In this sentence, þokan is the subject, so it is in the nominative singular.

Varð is the past tense of verða, which means to become.

So:

• var = was
• varð = became

The sentence is saying the fog became thick, not simply that it was thick. A very natural English equivalent is got:

• Þokan varð þykk = The fog became/got thick

The dictionary form is þykkur = thick. But Icelandic adjectives change form to agree with the noun they describe.

Here the adjective is predicative: it comes after varð and describes the subject þokan. Since þokan is feminine singular nominative, the adjective appears as:

• þykk

This is normal after vera and verða.

Compare:

• þykk þoka = a thick fog
• þykka þokan = the thick fog
• þokan varð þykk = the fog became thick

So the form changes depending on how the adjective is used.

Svo ... að is a very common pattern meaning so ... that.

In this sentence:

• svo þykk ... að við biðum ...
  = so thick ... that we waited ...

This expresses a result or consequence.

So svo here is not just so in the casual English sense. It is part of the structure:

• svo + adjective + að + clause

If you only wanted to say very thick, you would more likely use mjög:

• mjög þykk = very thick

But svo þykk að ... means so thick that ...

The preposition við here means by, at, or near. This preposition takes the accusative.

So:

• ströndin = the shore/coast/beach (nominative)
• ströndina = the shore/coast/beach (accusative)

That is why the sentence has við ströndina.

A natural translation is:

• by the shore
• at the coast
• sometimes by the beach

No. They are two different words that just happen to look the same.

In the first part:

• við ströndina
  við = a preposition meaning by/near/at

In the second part:

• að við biðum
  við = the pronoun we

This is very common in Icelandic: short words can have completely different functions depending on context.

Bíða means to wait. Its past tense is irregular.

Important forms are:

• ég beið = I waited
• við biðum = we waited
• þeir biðu = they waited

Because the subject is við = we, the sentence needs the 1st person plural past form:

• biðum

So:

• að við biðum = that we waited

The preposition í can take different cases depending on meaning:

• dative for location: in
• accusative for motion into something: into

Here the meaning is location: they were waiting in the car, not moving into the car. So Icelandic uses the dative:

• í bílnum = in the car

Compare:

• Við biðum í bílnum = We waited in the car
• Við fórum í bílinn = We went into the car

Here í is part of a time expression. Í smástund means for a little while.

So the sentence has two different í phrases:

• í bílnum = in the car
• í smástund = for a little while

Smástund is basically a short moment / a little while, from smá + stund.

Icelandic often uses í + time expression to mean for a duration:

• í klukkutíma = for an hour
• í smástund = for a little while

Because að introduces a subordinate clause, and subordinate clauses normally do not use the main-clause V2 word order.

So after að, the normal pattern is:

• að + subject + verb

That gives:

• að við biðum = that we waited

In a main clause, Icelandic often places the finite verb in second position, but after a subordinator like að, the structure is more straightforward.

Not necessarily. Við ströndina usually means by the shore, at the coast, or near the beach/shoreline.

It does not automatically mean that someone is physically standing on the sand. It is a broader location phrase.

So depending on context, English could use:

• by the shore
• at the coast
• near the beach

In this sentence, it introduces a result clause, not a purpose clause.

The idea is:

• The fog became so thick
• that we waited in the car

So it is describing what actually happened as a consequence.

English sometimes uses so that for both result and purpose, but here the meaning is clearly result:

• The fog got so thick that we waited in the car for a while

It is not saying they waited in order to do something. It is saying the thick fog caused that action.