Cada vez que miro por el microscopio, veo cosas que antes no veía.

Cada vez que means every time or whenever.

It introduces a repeated situation:

• Cada vez que estudio, aprendo algo nuevo.
• Cada vez que miro por el microscopio, veo cosas...

In this sentence, it means that on every occasion when I look through the microscope, the same general result happens.

With this meaning, Spanish normally uses the indicative, because it is talking about something real or habitual.

Spanish often omits subject pronouns when the verb ending already makes the subject clear.

So:

• miro = I look
• veo = I see
• veía = I used to see / I was seeing

Because the verb forms already show that the subject is I, adding yo is unnecessary unless you want emphasis or contrast:

• Yo miro por el microscopio, pero tú no.

In the original sentence, leaving out yo sounds completely natural.

This is a very common question.

• mirar = to look
• ver = to see

So in the sentence:

• miro por el microscopio = I look through the microscope
• veo cosas = I see things

The idea is: first you direct your eyes somewhere (mirar), then you perceive something (ver).

English works similarly with look and see.

Here por means something like through.

So:

• mirar por el microscopio = to look through the microscope

This is natural Spanish. You may also hear a través del microscopio, but por el microscopio is shorter and very normal.

Also, el microscopio refers to the microscope in the situation being discussed. If it were not specific, un microscopio could also be possible in another context.

Because the sentence contrasts what happens now with what used to be the case before.

• miro and veo are present tense: this is what happens now, habitually.
• veía is imperfect: it describes a past ongoing state or repeated past situation.

So the structure is roughly:

• Now: every time I look, I see things
• Before: I didn’t use to see those things

The imperfect is very natural here because it is not talking about one single moment in the past, but about a past situation over time.

Because vi is the preterite, which usually points to a completed event at a specific time:

• Ayer no vi nada. = Yesterday I didn’t see anything.

But veía is the imperfect, which describes a past condition, habit, or repeated situation:

• Antes no veía esas cosas. = Before, I didn’t use to see those things.

In your sentence, the speaker is comparing the present with an earlier period in general, not with one finished event. That is why veía fits better than vi.

The two que words do different jobs.

1. cada vez que
   Here que is part of the fixed expression cada vez que = every time that / whenever

2. cosas que antes no veía
   Here que is a relative pronoun, meaning that or which:

   • things that I didn’t see before

So even though the same word appears twice, it is not the same grammatical function both times.

The word que already refers back to cosas.

In:

• veo cosas que antes no veía

the relative clause que antes no veía means:

• that I didn’t use to see before

So que is already standing in for cosas as the object of veía. Because of that, you do not need another object pronoun.

English does something similar:

• I see things that I didn’t see before

You do not say things that I didn’t see them before. Spanish works the same way here.

Both word orders are possible, but they can sound slightly different in emphasis.

• antes no veía puts before earlier, highlighting the contrast with now
• no veía antes is also understandable, but may sound a bit less natural in this sentence

Spanish word order is often flexible, especially with adverbs like antes, but the original version flows very naturally because it sets up the contrast clearly:

• now I see things
• before I didn’t

The accent mark shows the correct pronunciation: ve-Í-a.

Without the accent, the letters might be read together differently. The accent tells you that the i is stressed and forms its own syllable.

So:

• veía = ve-í-a

This is common in forms of verbs like ver, oír, caer, etc., where the pronunciation needs to be marked clearly.

Yes, it is normal and correct here.

The first part:

• Cada vez que miro por el microscopio

is an introductory subordinate clause. In Spanish, when that kind of clause comes before the main clause, a comma is commonly used:

• Cada vez que miro por el microscopio, veo cosas...

If you reversed the order, the comma would often disappear:

• Veo cosas que antes no veía cada vez que miro por el microscopio.

But that version is less clear and less natural. The original order with the comma is much better.