「見えない」and「見られない」 How are they similar, what do they mean?

「見えない」と「見られない」

The best way to see the difference between 見えない and 見られない is through examples:

微粒子は肉眼ではほとんど見えない。
Minute particles are hardly visible to the naked eye.

彼は片目が見えない。
He is blind in one eye.

肉眼ではほとんど見えない星もある。
Some stars are hardly visible to the naked eye.

ここじゃないと見えないんだ。
I can only see it (the game) from here.

彼女は彼に涙を見られないようにした。
She turned away so he could not see her tears.

彼のような人は二度とは見られないだろう。
We shall not see his like again.

今晩は星１つ見られない。
Not a single star is to be seen tonight.

Expressions

二目と見られない。（ふためとみられない）
Can’t take another look, unable to look at it twice (the sight is unbearable).

見られたものではない。
When something is so crude that it cannot be looked upon at all.

Definitions of 「みえる」

「見える」の定義

① Shine-project into the eye. Confirmable by the eye.

② Visible. Able to be immediately perceived by eye.

③ Discernable. Able to catch sight of.

④ To be discovered, to be found.

⑤ Humble language to explain meeting someone. = I was able to see X.

Definitions of 「みられる」

「見られる」の定義

① To be visible. To recognize some situation. To think in such fashion.

② To be worthy of watching or viewing. To be valuable viewing.

③ Passive tense where Influential Actor is marked by に : To be seen. To be seen by someone. e.g. Someone に見られた。

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Research depicts many overlaps between 「みえる」and「みられる。」