Preheat oven to 375 degrees F. Grease and flour one 9-inch round cake pan.
Place flour, sugar, 1/4 cup brown sugar, water, vegetable oil, pineapple juice, vinegar, baking soda, and vanilla in mixing bowl; mix until batter is smooth. Pour batter into prepared pan. Bake for approximately 30 minutes, until a wooden pick inserted into the center of the cake comes out clean. Cool in pan 10 minutes, then invert onto serving platter.
To make glaze, place drained pineapple, apricot preserves and remaining 1/4 cup brown sugar in a small saucepan. Cook over medium heat, stirring constantly, until preserves are melted and bubbly. Slowly spoon the glaze evenly over the cooked cake. Allow to cool completely before serving.