If you want to know the extension of selected file from file chooser here is a code..
String fileName = file1.getName();
String fileExtension = fileName.substring(fileName.lastIndexOf(".") + 1, file1.getName().length());
System.out.println(">> fileExtension" + fileExtension);
And here is a brief of what you need to do with file chooser,
FileChooser fileChooser = new FileChooser();
// Set extension filter
FileChooser.ExtensionFilter extFilter = new FileChooser.ExtensionFilter("Image Files", "*.jpg", "*.jpeg");
fileChooser.getExtensionFilters().add(extFilter);
File file = fileChooser.showOpenDialog(root.getScene().getWindow());
if (file != null) {
String fileName = file.getName();
String fileExtension = fileName.substring(fileName.lastIndexOf(".") + 1, file.getName().length());
System.out.println(">> fileExtension" + fileExtension);
}