When to catch an exception?

Question

I have a getter method which is called from a "main" method in my class. This "main" method controls the functionality in my class. The getter method calls another method which can throw an exception.
Should I catch the exception and exit the program from the getter method or let this exception bubble through the getter method and be handeled by the "main" method?

Answer 1

Or like this?
public class test {
     private void doEverthing(){
               String string  = getMyArrayList();
     private String getMyArrayList(){
          try {
               String string = methodWhichThrowsException();
          } catch (Exception e) {
               // TODO Auto-generated catch block
               e.printStackTrace();
          return new String();
     private String methodWhichThrowsException() throws Exception{
          throw new Exception("aaa");
     public static void main(String[] args) {
          test t = new test();
          t.doEverthing();
}