Водоросли появились на стекле.

Yes, Russian has a singular form, водоросль, but in everyday usage водоросли is very common when talking about algae as growth on a surface, in water, and so on.

So in this sentence, водоросли means something like algae growth, not necessarily several clearly separate individual plants.

• водоросль = one alga / one strand / one specimen
• водоросли = algae in general, algae growth

This is similar to how English often prefers algae rather than an alga in normal speech.

It is nominative plural, because it is the subject of the sentence — the thing that appeared.

You can tell it is the subject because the verb появились agrees with it in the plural.

In the Russian past tense, the verb agrees with the subject in number, and in the singular it also agrees in gender.

Since водоросли is plural, the verb must also be plural:

• водоросли появились = the algae appeared

Compare:

• пятно появилось = a spot appeared
• водоросли появились = algae appeared

So the -ли ending shows plural past tense.

Появились comes from появиться, which means to appear, to show up, or to come into being / become present.

So the sentence does not just say that the algae were on the glass. It says that they appeared there — they were not there before, and now they are.

Compare the nuance:

• Водоросли были на стекле. = The algae were on the glass.
• Водоросли появились на стекле. = The algae appeared on the glass.

So появились focuses on the change of state.

Появились is perfective.

The infinitive is появиться. The imperfective partner is появляться.

Here the perfective is used because the sentence refers to a completed result: the algae have now appeared on the glass.

Compare:

• появились = appeared, came into view, came to be there
• появлялись = were appearing, used to appear, would appear repeatedly

So this sentence presents the appearance of the algae as a completed event.

Yes, появились is a reflexive verb form, from появиться.

But that does not mean it is literally reflexive in the English sense of did something to themselves. In Russian, -ся / -сь often appears in verbs that are not translated with self.

Here it is just part of the normal verb появиться = to appear.

So you should learn появиться as a whole vocabulary item, not try to translate it word-for-word as something like showed themselves.

Because на can take different cases depending on the meaning:

• на + prepositional = location, on
• на + accusative = motion onto something

Here the algae are located on the glass, so Russian uses the prepositional case:

• на стекле = on the glass

If you were talking about movement onto the glass, you could get the accusative:

• на стекло = onto the glass

So:

• Водоросли появились на стекле. = The algae appeared on the glass.
• location, not movement

It is the prepositional singular of стекло.

The pattern is:

• nominative: стекло
• prepositional: на стекле

This happens because на is expressing location here.

Literally, стекло means glass.

In context, it can mean:

• a glass surface
• a pane of glass
• window glass
• aquarium glass
• some other glass surface

Russian often leaves this kind of detail to context. So на стекле could mean on the window, on the pane, or on the glass surface, depending on the situation.

Yes. Russian word order is flexible.

This sentence is perfectly normal:

• Водоросли появились на стекле.

But you could also say:

• На стекле появились водоросли.

Both are grammatical. The difference is mainly one of focus or information structure.

A rough way to think about it:

• Водоросли появились на стекле. = neutral statement about the algae
• На стекле появились водоросли. = emphasis first on the location, on the glass

English usually depends more on fixed word order, but Russian uses word order more freely to shape emphasis.

It usually does not show that directly, because Russian has no articles like a and the.

So на стекле can mean:

• on the glass
• on a glass surface
• on the pane

Context tells you which one is meant.

That is very normal in Russian.

The stress is:

• во́доросли
• появи́лись
• на стекле́

So the whole sentence is pronounced:

Во́доросли появи́лись на стекле́.

For an English speaker, the most important thing is to notice that the stress is not always where you might guess from spelling.