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For example, stackexchange.com, without asking the site owner or Google their information about developing the website, is this possible to know what language is used in the back end?
Seems, the website don't have .extension bar, for example .php that can indicated which is developed in PHP, but without the extension, how can I know that?
There are indicators. Some are easier to find, others are harder.
.php indicates that the site is written in PHP, .asp indicates classic ASP, .aspx indicates ASP.NET, .jsp indicates Java JSPs, ...JSESSIONID is a widely used cookie name in Java serversBut all of those can be remove/changed/faked. Some are easier to change than others, but none are 100% reliable.
There are various reasons to change those indicators:
Well, there is the humans.txt file that a developer can put up on the domain that gives some information about the site development, maybe who worked on it and what standards or tools were used. If they want you to know about those kinds of information, they could/should put it there. However, just like anything else this is optional so it can't guarantee to inform you either. Check out humans.text
No, it could rather hard if not impossible if the webmaster doesn't want to disclose. There are some characteristics of few frameworks, but they can be hidden.
file extensions: there is no real reason to use standard ones, and most modern MVCs use URL routing anyway. So unless site has been around for some time, you're probably not going to see any (eg. stackexchange does't use .aspx extension);
session IDs: for example PHPSESSID is default for PHP, but can be easily overridden;
headers with web server and scripting language versions: can be turned off or even faked.
Stuff that's harder to hide:
[] to the name, thus you'd see something like: ...?var[]=1&var[]=3&.... AFAIK, it's the only web framework which handles it that way. I don't know if this specifically answer your question but there is a tool that was really helpful to me: Wappalyzer. It is a Firefox/Chrome extension that uncovers the technologies used on websites. It detects content management systems, web servers, JavaScript frameworks, analytics tools and many others. I know is not precisely what you are looking for but it give you a very close idea of what a site use. This is what it shows for programmers.stackexchange.com
In short: It is possible to hide what language you are using on the back-end. Trivial example: consider a "Hello World" page; it'd be extremely difficult to figure out what framework / language was being used on the back-end (assuming the basic stuff like session cookies are manually set or not in use).
However, the point of frameworks is to save you having to re-implement functionality, and to make you work in a standardised way. Almost all frameworks have their specific little tell-tales which will give them away, if you look close enough. As others have pointed out, it is possible to try to hide these, by using configuration or re-implementing various standard features. Nevertheless, I'd argue that for large sites, it'd be extremely difficult to completely hide everything, and even if you accomplished that, you'd be using very little of your framework.
In summary, I'd say it's almost always possible to get a very good idea of what's being used underneath (with some careful examination and prodding). Hiding the framework used is possible, but quickly becomes infeasible for large sites.
The previous answers have some good examples of various tell-tales that frameworks and languages have. I'd like to add that various view engines have specific whitespace-related behaviour which can be used to identify them. The Razor engine used in MVC3+ has some fairly specific quirks which could be used to identify it, or at least, narrow down the list of suspects (again, you can side-step it, but then, are you using it?).
It is possible to write a site in such a way, that no clues about the server technology will be visible to the client.
However, when someone uses some frameworks, such as IceFaces for Java, it is practically impossible do do because you'll see something like that in your requests:
ice.submit.partial=true&ice.session=c4f4jxT36tM_38848488&ice.view=3&ice.focus=&rand=0.322803445
Much of other frameworks have their characteristic stamps in either page body or requests/responses. Find them, google and you'll have an answer.
However, in each language, if you choose to create HTML from scratch (in Java world an example would be velocity templates) or choose pure AJAX way, where server returns/accepts only JSON messages, and client is entirely in JavaScript - a hard way, until you cause uncatched exception that reveals the technology under.
On sites which uses full-blown framework or CMS, sometimes you can try querying the admin page, you'll be presented with a login box and identify what framework it came from because most people don't reskin the admin template. For instance if your site is example.com, try going to example.com/admin/ or example.com/wp-admin/ (wordpress).
You should check out this site: Built With. It lets you know all that information if available.
No it is not possible to find language used in the websites by viewing the source code of the web page and search the existence of languages. because of usage of more than one languages for creation of website to provide high security
.phpto a CGI-Script written in C or a Servlet written in Java.