Ég ætla að láta gera ný gleraugu eftir sjónprófið.

It means I intend to or I’m going to.

In Icelandic, ætla að + infinitive is a very common way to talk about a plan or intention:

• Ég ætla að fara = I’m going to go
• Ég ætla að kaupa þetta = I’m going to buy this

So:

• Ég ætla að láta gera... = I’m going to have ... made

It is not a future tense in the same way as English will, but in many situations it works like be going to.

This is a causative structure. It means to have something done or to get something done by someone else.

So:

• láta gera ný gleraugu = have new glasses made

The speaker is not making the glasses personally. The idea is that someone else, such as an optician or lab, will make them.

A useful comparison:

• Ég geri gleraugu = I make glasses
• Ég læt gera gleraugu = I have glasses made

Because the two verbs work differently.

• ætla normally takes að + infinitive
• láta is followed by a bare infinitive in this kind of causative construction

So:

• ætla að láta
• láta gera

Not:

• *láta að gera

This is similar to how English says make someone do something, not make someone to do something.

Because láta has several related uses, and one of the most common is this causative one.

It can mean:

• let / allow
• make / cause
• have something done

In this sentence, the meaning is clearly the causative/service meaning:

• Ég ætla að láta gera ný gleraugu
  = I’m going to have new glasses made

So even though láta is often introduced as let, learners quickly meet sentences where it is better translated as have.

Because gleraugu is normally a plural-only noun in Icelandic, just like glasses in English.

So even when you mean one pair of glasses, Icelandic still uses the plural form:

• gleraugu = glasses / a pair of glasses

That is why the adjective also appears in the plural:

• ný gleraugu = new glasses

Because the adjective has to agree with the noun.

Gleraugu is:

• neuter
• plural

So the adjective must also be neuter plural:

• ný = neuter plural (and also some other forms)

That gives:

• ný gleraugu = new glasses

If the noun were singular neuter, you would expect nýtt, but that is not the form needed here.

It is in the accusative, because it is the thing affected by láta gera.

Here the speaker is going to have new glasses made, so ný gleraugu functions as the object.

A detail that can confuse learners: for this noun phrase, the nominative and accusative forms look the same, so you do not see a visible change here.

Because Icelandic usually puts the definite article at the end of the noun as a suffix.

So:

• sjónpróf = eye test / vision test
• sjónprófið = the eye test

Also, sjónpróf is a compound noun:

• sjón = vision / sight
• próf = test

So sjónprófið literally means the vision test.

This means after the eye test.

• eftir = after
• sjónprófið = the eye test

So the phrase tells us when the speaker plans to have the glasses made.

In other words, the timeline is:

1. first the eye test
2. then getting the new glasses made

Icelandic is focusing here on the idea of having the glasses made/prepared, not simply purchasing them.

That fits the real-life situation well: after an eye test, you usually have glasses made to your prescription.

So:

• kaupa gleraugu = buy glasses
• láta gera gleraugu = have glasses made

The second version emphasizes the service/process, not just the transaction.

Yes. Icelandic word order is fairly flexible, especially with time expressions.

For example, you could also say:

• Eftir sjónprófið ætla ég að láta gera ný gleraugu.

That still means the same thing: After the eye test, I’m going to have new glasses made.

When a phrase like eftir sjónprófið comes first, Icelandic normally puts the finite verb next:

• Eftir sjónprófið ætla ég...

This is part of Icelandic’s common verb-second pattern.

Usually it means they plan to or intend to do it.

• Ég ætla að... is about intention
• it often sounds strong, but it is still basically a plan

So the sentence suggests something like:

• I’m planning to have new glasses made after the eye test
• I’m going to have new glasses made after the eye test

It is not necessarily a solemn promise, just a clear intention.