I have one 'select' menu with certain options..

Lets say Option 1, Option 2, Option 3, & Option 4 -->

Code:
<select name="options" id="options">
                  <option value="option1">Option 1</option>
                  <option value="option2">Option 2</option>
                  <option value="option3">Option 3</option>
                  <option value="option4">Option 4</option>
                </select>
I have another menu directly below it. When Option 1 is selected on the top menu, I want the second menu to display certain options, but when Option 2 is selected on the top menu I want there to be a different set of options in the second menu...

I am not sure how I should go about doing this. I don't want the page to have to be refreshed.

Could anyone shed any light on how i might do this?