Measure the height, depth and width of the area where the cabinet will be built, using a tape measure. Write the measurements on a sheet of paper. Place a sheet of 1-inch thick mica on a flat surface with the laminated side up. Measure and draw out a rectangle the height and depth of the cabinet on the laminated surface, using a pencil and ruler.
Move any supports holding the Formica level so the wood is supported close to both sides of the marked lines you are about to cut. Hold a dovetail saw at a low angle to the formica. Cut along the marked lines using the dovetail saw, making sure to keep the angle of the saw low against the wood to prevent the laminate splitting.
Repeat steps 1 and 2 to create a second rectangle from the 1-inch thick mica. These will be the cabinet sides.
Measure and cut two sheets of mica as long as the width of the cabinet minus 2 inches, and as wide as the depth of the cabinet. These will be the top and bottom of the cabinet. Fit the 1/2-inch diameter drill bit to the hammer drill. Drill three 1/2-inch deep holes in both ends of both sheets.
Cut the 1/2-inch diameter dowel rod into 12 1-inch long pieces. Apply wood glue around each piece. Tap the dowel pieces into the holes drilled in the ends of the two cabinet-length pieces, using a hammer. Hold the pieces against the top and bottom of the cabinet-height pieces so the depth-length edges of the cabinet-height pieces are flush with the laminated side of the cabinet-length pieces.
Mark the points where the dowel pieces touch the cabinet-height pieces, using a pencil. Drill a 1/2-inch deep hole at each of the market points. Fit the ends of the dowel pieces into the holes. Tap the cabinet-length pieces with a hammer until the dowel pieces are fully inside the sheets, forming a solid cabinet frame. Ensure the sheets are aligned so the laminated faces are on the front and outside of the cabinet.
Cut a sheet of 1/2-inch thick plywood according to the width and height measurements of the cabinet, using a circular saw. Nail the sheet to the open face of the cabinet frame where the the wooden core of the mica is exposed, using 1-inch long nails. This forms the back of the cabinet.
Measure and cut one sheet of 1-inch thick mica as long as the width of the cabinet minus 2 inches, and as wide as the height of the cabinet minus 1 inch. Draw a width-long line across the middle of this mica sheet, using a pencil and ruler. Cut along this line with the dovetail saw.
Screw a cabinet door handle to the laminated face of the mica, in the middle of one width-long edge on both halves of the sheet, using a screwdriver. Screw two hinges to the non-laminated face, equidistant from the half-cabinet-width edges and on the edge opposite to the handles. Screw the other wing of the hinges to the inside face of the cabinet side panels, to install the doors and complete the cabinet.