Someone in authority apologizes?

Question

I am looking for examples where someone in authority apologizes to someone lower than him. I am specifically looking for examples where we know that the authority figure is someone to emulate (eg. the story is brought in the gemara, or in a mussar work, etc.).

For example did Hashem ever apologize?
How about a King?
How about others?

Examples please

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Edit

Still looking for an answer.
(DanF's answer does not show that Rav Elazar had authority,
b-a's answer does not show an explicit apology only a repayment for damages an implicit one,
mbloch's answer is an answer but it is possible that the child was not under the Steipler's authority,
Alex's answer clearly is saying that you need to apologize to a friend/neighbour and not regarding someone subordinate to you,
Gary's answer it seems pharoah by apologizing accepted the authority of G-d and Moses not that he was not apologizing from a position of authority.)

Answer 1

See Talmud Ta'anit 20a - 20b. Synopsis:

Rav Elazar ben Rav Shimon was on the road and an ugly man greeted him. Rav Elazar offended him by asking, "Are all people from your village as ugly as you?" He had to follow the man to his town begging for forgiveness.

The maxim that Rav Elazar himself states, on p. 20b, after he apologized and realized his error, is an important behavior to emulate.

Answer 2

For example did Hashem ever apologize?

Chulin 60b tells of how God tried to appease the moon after diminishing it, and eventually ordains the new month's sacrifices as a sin offering for his having diminished it.

רבי שמעון בן פזי רמי כתיב (בראשית א, טז) ויעש אלהים את שני המאורות הגדולים וכתיב את המאור הגדול ואת המאור הקטן אמרה ירח לפני הקב"ה רבש"ע אפשר לשני מלכים שישתמשו בכתר אחד אמר לה לכי ומעטי את עצמך אמרה לפניו רבש"ע הואיל ואמרתי לפניך דבר הגון אמעיט את עצמי אמר לה לכי ומשול ביום ובלילה אמרה ליה מאי רבותיה דשרגא בטיהרא מאי אהני אמר לה זיל לימנו בך ישראל ימים ושנים אמרה ליה יומא נמי אי אפשר דלא מנו ביה תקופותא דכתיב (בראשית א, יד) והיו לאותות ולמועדים ולימים ושנים זיל ליקרו צדיקי בשמיך (עמוס ז, ב) יעקב הקטן שמואל הקטן (שמואל א יז, יד) דוד הקטן חזייה דלא קא מיתבא דעתה אמר הקב"ה הביאו כפרה עלי שמיעטתי את הירח והיינו דאמר ר"ש בן לקיש מה נשתנה שעיר של ראש חדש שנאמר בו (במדבר כח, יא) לה' אמר הקב"ה שעיר זה יהא כפרה על שמיעטתי את הירח

“Rabbi Shimon ben Pazzi notes a contradiction: ‘And God made the two great lights; but it also says ‘The large light, and the small light.’

The moon said to the Holy One, Blessed Be He, ‘Master of the Universe, How can two kings share one crown?’

He said to her, ‘Go and diminish yourself!’

She said to him: ‘Master of the universe, because I said a logical thing before you, I should diminish myself?’

He said to her, ‘Go and you will rule by day and by night’.

She said to him, ‘What is the greatness in that? How does a lamp help in the daytime?’

He said to her: ‘Go! Israel will count through you the days and the years.’

She said to him, ‘Day is the primary unit of time, and I can’t be used to count for days, as it says “And let them be for signs of the seasons and days and years”.’

He said, “Go! And great people will be called by your name: ... Yaakov the Small, Shmuel the Small, David the Small."

God saw that the moon was still not happy at the time. The Holy One said, “Bring an atonement for Me, for I have diminished the moon.”

And so that is what is meant when Rabbi Shimon ben Lakish said, “What is the difference in how the New Moon offering is written, “A he-goat on the new moon, for the Lord?’ Because the Holy One is saying, ‘Let this he-goat be an atonement for me, for the diminishment of the moon.”

_{(Sefaria translation with slight changes)}

Answer 3

There are many stories of great rabbis apologizing to people much below their spiritual level. For instance, this story of the Steipler Gaon apologizing to a bar mitsva boy for mistakenly criticizing him six years earlier (written up by R Mordechai Kamenetzky on torah.org)

In the city of B’nai Beraq there are many Bar Mitzvah celebrations every Shabbos. It became very difficult for Rav Yaakov Yisrael Kanievski, the elder sage known to world Jewry as the Steipler Gaon to attend every Bar Mitzvah. In fact, he was old and weak and hardly had the strength to go to shul. One week, a Bar Mitzvah boy was honored with the maftir. Immediately after the davening, the Steipler Gaon was standing there in line, waiting to wish him Mazal Tov.

The Steipler Gaon bent down and began conversing in earnest with the neophyte member of the adult Jewish community. It seemed to the hushed crowd that this was much more than a perfunctory Mazel Tov wish.

The boy paled as he shook his head several times in amazement. “Of course, Rebbe!” he exclaimed. “Of course! There is no question. I feel terrible that the Rebbe felt he had to discuss this with me!”

The Steipler thanked the young boy, wished him Mazel Tov again, blessed him, and left the shul.

The entire congregation was shocked. What could the Steipler have wanted?

“Let me explain,” began the boy. “Six years ago I was davening in this shul with a very large siddur (prayer book). The Steipler approached me and chided me for learning Gemara in the middle of the Tefilah. I showed him that it was a Siddur and that I actually was davening. He apologized and left.

Today the Steipler came to my Bar Mitzvah and reminded me of the story. He explained to me that even though he apologized for his mistaken reprimand six years ago, it was not enough. Since, at the time, I was a child under Bar Mitzvah, I did not have the frame of mind to truly forgive him. Even if I did forgive him, it had no halachic validity. The Steipler found out when my birthday was and waited for six years until my Bar Mitzvah. Today, I am halachically old enough to forgive him, and so, he came back today to ask my forgiveness!”

See also this long but very interesting article (Facing the truth of history) where, at the very end, R Jacob J Schachter, a professor at YU, describes how he went in front of the grave of R Yechiel Yaakov Weinberg, the Seridei Aish, to apologize for possibly causing him anguish through something R Schachter wrote - and apologizes again in writing.

Answer 4

Berachot 31b

ויען עלי ויאמר לכי לשלום אמר רבי אלעזר מכאן לחושד את חברו בדבר שאין בו שצריך לפייסו ולא עוד אלא שצריך לברכו שנאמר ואלהי ישראל יתן את שלתך

Then Eli answered and said, Go in Peace. R. Eleazar said: From this we learn that one who suspects his neighbour of a fault which he has not committed must beg his pardon; nay more, he must bless him, as it says, And the God of Israel grant thy petition. (Soncino translation)

Answer 5

After the plague of locusts, Exodus/Shemot 10:16-17 (Chabad translation) has Pharoah apologizing:

Pharaoh hastened to summon Moses and Aaron, and he said, "I have sinned against the Lord your God and against you. But now, forgive now my sin only this time and entreat the Lord your God, and let Him remove from me just this death."

It doesn't fit your qualification of an example of someone to emulate, but it's a King apologizing.

There's some Kings apologizing to Prophets later on, Saul asking forgiveness from Samuel(or HaShem, via Samuel)in the matter of sparing Agag, etc.

Found one that sounds like it might be interpreted as an apology from HaShem(even though in the Agag episode Samuel says HaShem does not repent like a man):

Jeremiah 42 9-12, where it appears HaShem is repenting for what he did to the Jewish people, and is willing to make up for it IF the remnant of Judah does not go to Egypt.

And he said to them: "So said the Lord God of Israel, to Whom you have sent me to present your supplication before Him. If you dwell in this land, I will build you up and I will not pluck you up, for I have repented of the evil that I have done to you. Fear not the king of Babylon whom you fear; fear it not, says the Lord, for I am with you to redeem you and to save you from his hand. And I will give you mercy, and he shall have mercy on you, and he shall return you to your land."

They didn't believe Jeremiah and did go to Egypt, unfortunately...but it sure does sound like an apology and olive branch from HaShem - and an example to emulate, as best we can.