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General laws of Brachot on Sights
If one saw a friend one a television or heard them on the phone or radio, one doesn’t make any Bracha for seeing or hearing them. 
All the below Brachot for certain sights are made if one hasn’t seen them in thirty days or more. 
Seeing from a distance or airplane is still considered good enough vision in order to make the bracha as long as one can see the sight clearly and the sight is recognizable. 
Seeing a sight at night warrants a Bracha as long as one the sight is distinguishable even at night. 
Some say one can still make the Bracha upon seeing a wonder of nature even after one has left as long as the sight still impresses or inspires oneself.  Some say that one may make the Bracha only while one is still in the area where one can still see the sight or if it’s within the Toch Kedi Dibbur of leaving that area. 
Bracha for seeing Glamorously Rebuilt Jewish Settlements
Though the Gemara says that one may recite the Bracha "Matziv Gevul Almanah" upon seeing settled Jewish communities, many contemporary Poskim advise leaving out Hashem's name, due to the variety of opinions regarding the required conditions. Still, a number of Poskim permit reciting the Bracha in Eretz Yisrael.
Bracha for seeing a house of Avoda Zara
Nowadays we do not make the Bracha for seeing a house of Avoda Zara (which was Baruch Atta…SheNatan Erech Apayim LeOvri Retzono). 
Bracha for Seeing a Scholar
For seeing a great Jewish Chacham (wise scholar) the Bracha is Baruch Atta… SheChalak MeChachmato LeYire’av ברוך אתה ה' אלקינו מלך העולם שחלק מחכמתו ליראיו  Some say that this beracha should not be said with Hashem's name.  Anyway, this Bracha is made rarely because it should only be made for a wise scholar, G-d fearing person, and man of Middot. 
For seeing a brilliant non-Jewish secular scholar the Bracha is Baruch Atta… SheNatan MeChachmato LeBasar VeDam.  Some say that there’s a minhag not to make this Bracha nowadays. 
Bracha for seeing a king or queen
It is a mitzvah to go and see rulers and kings, whether they are Jewish or non-Jewish. Nonetheless, one shouldn't waste time from learning to do so unless the king came with special pome and grandeur.
Upon seeing a Jewish king one should recite ברוך אתה ה' אלוקינו מלך העולם שחלק מכבודו ליראיו (Baruch... Shechalak Mikvodo Liyireav). 
Upon seeing a non-Jewish king one should recite ברוך אתה ה' אלוקינו מלך העולם שחלק מכבודו לבשר ודם (Baruch... Shenatan Mikvodo LeBasar vaDam). 
It is questionable if nowadays one should make this Beracha for seeing a king, queen, president, or prime minister, and therefore one should only make this Bracha without Shem UMalchut. 
This Bracha applies equally to a male king as to a female queen, however, one shouldn’t stare at the queen but only a quick look. 
Seeing the monarch on television would not obligate you in the beracha. 
Bracha for seeing a cemetery
For seeing a Jewish cemetery the Bracha is Baruch Atta…Asher Yatzer Etchem…Mechaye Maytim. ברוך אתה ה' אלוקינו מלך העולם, אשר יצר אתכם בדין ודן אתכם בדין וכלכל אתכם בדין והחיה אתכם בדין, ואסף אתכם בדין, ויודע מספר כולכם, ועתיד להחיותכם ולהקימכם בדין לחיי העולם הבא, ברוך אתה ה' מחיה המתים Some say that this beracha should not be said with Hashem's name.  This Bracha can be made for seeing it through glass and so if one see a cemetery from a car while driving one can make this Bracha.  Some say that one may make the Bracha even after leaving the sight as long as one is still effected and impacted by it. 
Bracha for seeing a friend
Nowadays, the Ashkenazic minhag is not to make a bracha upon seeing a friend after 30 days or after 12 months. 
However, some say Sephardic minhag is to make the Bracha of Shehecheyanu even if one was in contact as long as one hasn’t seen them for 30 days, while some disagree. 
Bracha for seeing 600,000 people
Upon seeing 600,000 Jews there’s a Bracha of Baruch Atta…Chacham HaRazim, however, this is a extremely rare occurrence. 
Upon seeing 600,000 non-Jews one should say the פסוק “Boshu Imachem Meod…” and some say that one can say this for any gathering of non-Jews. 
↑Berachot 58b, Shulchan Aruch 224:10. Rav Chaim David HaLevi (vol 4 Siman 5) does not allow one to recite the Berach ever with Shem uMalchut; Rav Mordechai Eliyahu (Ma'amar Mordechai vol. 3 Kedushat HaAretz Siman 3) seems to hold that way, as well. Similarly, Rav David Yosef (Halacha Berurah 224:21) recommends one say it bli shem umalchut upon seeing fine homes and synagogues, either in Eretz Yisrael or Chutz LaAretz, as a Chumra for Rashi's shitah that it's only BaZeman HaBayit. However, Piskei Teshuvot (224:9) concedes that one who does recite the Beracha on glamorous Batei Kenesiot and Batei Midrashot in Eretz Yisrael isn't out of line. Rav Meir Mazuz might also be lenient. See Mishneh Halachot 10:75.
Rav David Lau recited the bracha in front of Rav Dov Lior when the community of Asa'el a few years back grew and officially installed Rav Meir Bareli as rabbi. HaRav Hershel Schachter recited the Beracha when visiting Yeshivat Elon Moreh, and Rav Eliezer Melamed did when speaking in Yeshivat HaGolan. Rav Dov Lior and Rav Chaim Druckman have also done so on similar occasions.
The aforementioned Rav Meir Bareli himself wrote an article in HaMaayan (Tishri 5771, 51-1, page 39) on this very topic. See R' Melamed's article and Peninei Halacha, as well as R' Yehuda Amichai's article for more.
↑ S”A 224:1 writes that for seeing an Avoda Zara the Bracha is Baruch Atta…SheNatan Erech Apayim LeOvri Retzono. The Mishna Brurah 224:2 adds that this Bracha also applies if one only sees the house of the Avoda Zara. However, the Rama 224:1 writes clearly that our minhag is not to make this Bracha nowadays since we see these houses of Avoda Zara often. Mishna Brurah 224:3 extends the case to even if one didn’t see the house of Avoda Zara in thirty days one still doesn’t make the Bracha.
↑S”A 224:6, Berachot 58a, Kitzur Shulchan Aruch 60:9, Rambam Berachot 10:11, Yechave Daat 4:16, Chayei Adam 63:5. Even though the Rambam's text is SheNatan MeChachmato even for Jewish scholars, the halacha is to follow the text of the gemara which is SheChalak for Jews (Yachava Daat 4:16).
Aruch HaShulchan OC 224:6 says not to make this beracha nowadays since we are not sure if the talmidei chachamim are as great as the talmidei chachamim to which the gemara refers. Also, Ben Ish Chai Parashat Ekev: Halacha 13, Tzitz Eliezer 14:37:3, Chesed Laalafim 224:12 suggest making a beracha without Hashem’s name. Kaf Hachaim 224:19 agrees. However, Yachava Daat 4:16 argues that the talmidei chachamim of each generation are considered like the greats of the previous generations (Rosh Hashana 25b).
However, the Piskei Teshuvot (224: note 17) lists many gedolim who made this beracha on others. It also quotes Rav Moshe Feinstein, Chacham Ovadia, Chazon Ish, Minchat Elazar 5:7 that one should make this beracha on rabbis today. Rivivot Ephraim 8:128:6 writes that one should recite the blessing upon seeing Rav Shach zt"l, Rav Elyashiv zt"l, and Rav Chaim Kanievsky shlit"a. Similarly, Rav Shmuel Wosner (Shevet Halevi 10:13) writes that he recalls that when the Rogachover Gaon visited Vienna, many recited the blessing upon seeing him. The Chazon Ish felt that the beracha should be recited on the Steipler (Orchos Rabbeinu 1:109). The Steipler (Sefer Orchos Rabbeinu (1:110) writes that he recited this blessing upon seeing the Chofetz Chaim zt"l and Rav Meir Simcha zt"l of Dvinsk.
↑Piskei Teshuvot 224:5 writes that the minhag is not to make this Bracha since some say that one should make the Bracha on non-Jews that don’t keep the 7 מצות of Bnei Noach.
↑The Gemara Brachot (9b, 19b, 58a) explains that a person should endeavor to see kings so that if he merits he will be able to distinguish between a regular king and Mashiach. Rambam (Avel 3:14) and Shulchan Aruch 224:4 codify this.
How much power does the ruler have to have in order to make the Bracha upon seeing him? Rav Ovadia Yosef Yechave Daat 2:28 cites the Radvaz 1:296 as well as the Orchot Chaim Berachot 49 that say that this beracha is recited on any monarch with enough power to execute or pardon from execution. Halacha Brurah 224:14 writes that one makes the Bracha (with Shem UMalchut) on a king of a country even if he is democratically elected and even if he is only ruler for a term as long as there isn’t a another figure above him that can nullify his decision such as if his decisions don’t need to be approved by parliament. Halacha Brurah mentions specically if the ruler has the power to pardon someone sentenced to death or declare war against another country then one may make the Bracha on that king with Shem UMalchut.
What about a President who doesn't wear royal clothing? Rav Ovadia Yosef in Sh”t Yabia Omer 8:22(25) rules that one doesn’t make the Bracha with Shem UMalchut if the king is wearing normal clothing (not royal clothes). Actually, Rav Ovadyah Yosef writes that when the US President Nixon came to Israel that they made the Bracha without Shem UMalchut because he was wearing normal clothes. Rav Moshe HaLevi in Birkat Hashem (vol 4 3:32) agrees. [See, however, Halacha Brurah 224:14 writes that even if the king isn’t wearing royal clothing but as long as he is recognizably respected by his officers that surround him and by the many people coming to see him, then one may make the Bracha with Shem UMalchut on such a king. Sh”t Elyashiv HaKohen 2:26 quotes Rav Mazuz who agrees with Halacha Brurah.]
Piskei Teshuvot 224:6,7 concludes that nowadays one should make this Bracha without Shem UMalchut for seeing a king, queen, president, or prime minister. Beer Moshe 2:9 agrees.
Shu"t Shevet Haleivi Vol. 1 Siman 35 writes that you should recite the beracha with shem umalchut on the president. See also Shu"t Minchas Elazar Vol. 5 Siman 7.
↑Halacha Brurah 224:15 quoting Sh”t Bear Moshe 2:9(4), 2:14(16), Sh”t Shevet HaLevi 1:35, Sh”t Rivevot Efraim 1:47(3), B’tzel Hachachma 2:19 and others who all make this distinction between staring and seeing based on Beit Yosef 75 d"h viasur. Rabbi Shlomo Zalman Braun in She’arim Metzuyanim B’halacha 1:60:7 rules however that one cannot recite the blessing over a queen because a man may never even gaze at a woman. See also Rav Moshe Shternbuch in Sh”t Teshuvot ViHanhagot 2:139 rules that since the obligation is based on the honor given to that monarch, that one should in fact recite the beracha upon seeing the monarch of modern day England, even a female despite the fact that we don't allow for a Jewish monarch to be a women.
↑ Yechave Daat 2:28 compares it to saying birkat halevana upon seeing the moon in the mirror, which we do not do based on the gemara in rosh hashana 24b and birkei yosef Choshen Mishpat 35:11. see also Sh"t Bitzel Hachochma 2:19, Beer Moshe 2:9
↑Halichot Shlomo 23:26 (in the footnote) writes that if one didn't make the bracha immediately upon seeing the Jewish cemetery, one may make the bracha as long as the sight effects oneself.
↑ Halichot Shlomo 23:12, Piskei Teshuvot 225:2. Mishna Brurah 225:2 says to recite shehecheyanu upon seeing a friend, parent, or teacher that one has not seen in 30 days as long as there hasn't been any correspondence.
↑Yalkut Yosef (vol 3 pg 605) writes that the minhag is to make both these Brachot under the conditions of S”A. However, Vezot HaBracha (pg 171) quotes Rav Mordechai Eliyahu who says that the minhag is not to make these Brachot nowadays.