2 Forms (select) - 1 is dependent from 2

I want create form in html+php. I have got 2 tables in my database.

1. Categories: id_category, category


2. Dairy: id_dairy, id_category, product_name

And now is question. How can I create 1 form with 2 select dropdowns. Is it possible to do it in PHP without AJAX?

I mean that - I want choose Category and then choose Products without refresh page.

Code:

<form role="form" action="kalorie.php" method="post">
      <div class="form-group">
        <label for="kategoria">Kategoria:</label>
        <select class="form-control" name="kategoria">
          <option>Wybierz kategorie</option>
            <?php
              $sql_1 = "SELECT * FROM produkty";
              $result_1 = mysqli_query($conn, $sql_1);

              while($row_1 = mysqli_fetch_assoc($result_1)) {
                echo '<option>'.$row_1["produkt"].'</option>';
              }

              $kat = $_POST['kategoria'];
            ?>
        </select>
        <select class="form-control" name="produkt">
          <option>Wybierz produkt</option>
            <?php
              $sql_2 = "SELECT * FROM $kat";
              $result_2 = mysqli_query($conn, $sql_2);

              while($row_2 = mysqli_fetch_assoc($result_2)) {
                echo '<option>'.$row_2["produkty"].'</option>';
              }
            ?>
        </select>
      </div>
      <button type="submit" class="btn btn-default" name="oblicz">Wyślij</button>
    </form>