haesbichi ganghalsurok mojaga kkok piryohae.

-ㄹ수록 means the more..., the more... or as ... more and more.

So 햇빛이 강할수록 모자가 꼭 필요해 means something like:

• The stronger the sunlight, the more necessary a hat is.
• As the sunlight gets stronger, you really need a hat.

Here, 강하다 becomes 강할수록:

• 강하다 = to be strong/intense
• 강할수록 = the stronger it is / the more intense it is

This pattern is very common in Korean:

• 비쌀수록 좋다고 생각하는 사람도 있어. = Some people think the more expensive it is, the better.
• 많이 할수록 늘어요. = The more you do it, the more you improve.

Both can work, but the nuance is slightly different.

• 강할수록 = the stronger it is
• 강해질수록 = as it becomes stronger

In many contexts, these are very close in meaning.

With 햇빛이 강할수록, the sentence sounds like a general statement about degree:

• The more intense the sunlight is, the more a hat is needed.

With 햇빛이 강해질수록, the sentence would focus a little more on change over time:

• As the sunlight becomes stronger, a hat becomes more necessary.

So the original sentence is natural and compact, especially for a general truth.

Here, 햇빛이 marks sunlight as the subject of 강하다.

• 햇빛이 강하다 = The sunlight is strong.

Using 이/가 is very normal when you are describing a condition or quality directly.

If you changed it to 햇빛은, it would add more of a topic/contrast feeling:

• 햇빛은 강할수록... might sound like as for sunlight, the stronger it is...

That is not impossible, but 햇빛이 강할수록 is the most straightforward and natural form here.

In this sentence, 강하다 means strong/intense in the sense of sunlight being harsh or powerful.

So 햇빛이 강하다 means:

• the sunlight is strong
• the sun is intense
• the sun’s rays are harsh

It does not mean that sunlight is strong like a person is strong.

Korean uses 강하다 with many things:

• 바람이 강하다 = The wind is strong.
• 냄새가 강하다 = The smell is strong.
• 빛이 강하다 = The light is strong/bright/intense.

꼭 adds emphasis. Here it means something like:

• definitely
• absolutely
• really
• must

So:

• 모자가 필요해 = A hat is necessary.
• 모자가 꼭 필요해 = A hat is definitely/really necessary.

It makes the statement stronger. It does not always mean strict obligation like must in every situation, but here it gives the feeling that a hat is very important.

Because 필요하다 works like to be necessary, and the thing that is necessary is often marked with 이/가 in Korean.

So:

• 모자가 필요해 = A hat is necessary.

This may feel different from English, because in English we often say:

• I need a hat

But Korean often expresses the same idea more like:

• A hat is necessary

That is why 모자 takes 가, not 를.

Some examples:

• 물이 필요해. = Water is needed.
• 시간이 더 필요해. = More time is needed.

필요해 is the conversational form of 필요하다.

• 필요하다 = dictionary form
• 필요해 = casual/informal speech
• 필요해요 = polite everyday speech
• 필요합니다 = formal speech

So the sentence could be changed depending on style:

• 햇빛이 강할수록 모자가 꼭 필요해. = casual
• 햇빛이 강할수록 모자가 꼭 필요해요. = polite
• 햇빛이 강할수록 모자가 꼭 필요합니다. = formal

The original sentence sounds like everyday spoken Korean.

Yes. Korean often leaves out subjects like I, you, or people when they are understood from context.

This sentence is a general statement, so it does not need an explicit person. It means something like:

• When the sunlight is stronger, a hat is definitely necessary.
• The stronger the sunlight, the more you need a hat.

English often inserts you in natural translation, but Korean does not have to.

Yes. -ㄹ수록 / -을수록 can be used with both.

With adjectives:

• 날씨가 더울수록 물을 많이 마셔야 해. = The hotter the weather, the more water you should drink.
• 비쌀수록 좋은 건 아니야. = The more expensive it is, the better it is not necessarily.

With verbs:

• 볼수록 재미있어. = The more I watch it, the more interesting it becomes.
• 연습할수록 늘어요. = The more you practice, the more you improve.

In your sentence, it is attached to the adjective 강하다.

Not exactly. 햇빛이 강하다 specifically focuses on the strength/intensity of the sunlight, not just whether it is sunny.

• sunnier usually refers to weather being more sunny or less cloudy
• 햇빛이 강하다 means the sun’s rays are stronger or harsher

So a better translation is:

• The stronger the sunlight, the more necessary a hat is.
• As the sunlight gets stronger, you really need a hat.

Yes, that is a very natural way to understand it.

Literally, it is closer to:

• A hat is definitely necessary.

But in real English, we often say:

• You really need a hat.

That kind of translation is often better because it sounds natural in English, even though Korean is structured differently.

So it is useful to remember both levels:

• Literal structure: A hat is definitely necessary.
• Natural English meaning: You really need a hat.