U.S. Plastic Corp. sells acrylic mirror sheeting that's UV stabilized, shatterproof, much stronger than glass, and withstands -40° F to 180° F. One 1/8"x 12"x 24" sheet ($16) yields four mirrors. Visit a local glass shop for a piece of clear 1/8" x 18" x 20" acrylic.
Leave the provided mirror-protecting film on throughout the project. Assuming you'll make four mirrors, for yourself and family or friends, use a table saw with a fine-toothed blade to cut four 2-½" x 16¼" strips, mirror side up. Also cut four strips of clear acrylic 2-½" x 19-1/4" for housing backs.
Make the housing
The housing holds the mirror in a slight convex undistorted bend, increasing the view field.
Make the housing back, using a wood fixture. On a table saw set to 60 degrees cut about a 2-½" strip from a 6" x 6" piece of ¾" wood. C-clamp the larger piece to your workbench at a 90-degree angle to another wood strip nailed in place. Then 1-½" from an end of the 19-1/4" acrylic strip, mask off a 1/8"-wide clear area with aluminum foil. Evenly heat the area both sides (with a heat gun or by holding over an electric stove element) until the acrylic becomes pliable, then use the narrow angled wood block to force the acrylic into an even 60-degree bend, keeping the edge of the back tight against the wood stop. Repeat at the other end. These are pockets for the ends of the mirror.
Measure the overall length of the back (after bending) and cut two 3/4"-wide acrylic strips (housing sides) to slightly more than that length. On both ends of each side strip, make a mark 1/2" from one edge. Then mark the center of the strip length. Slightly bend one of the side strips to use as a guide. Trace its curve onto the other side strip between the center and end marks. Repeat for the other side strip. Create the curve on both strips on a disc sander. On a band saw, cut two notches in each side strip opposite the curved side.
Cover your work surface with waxed paper and use Krazy Glue to bond only one side strip onto the back (for now). Adjust the mirror length by gradually trimming one of its ends squarely on a disc sander and repeatedly trial-fitting by sliding it into the housing until you measure the critical dimension A. Only then, glue on the other side strip. Trim excess acrylic from the tray with a band saw and/or disc sander. Don't install the mirror yet.
Smooth all edges and corners of the housing on a disc sander and by hand sanding. Fill minor flaws with Bondo Glazing Compound, let dry, and hand-sand smooth.
Glue two lengths of ½"-dia x 5-5/8" polyfoam lengthwise on the tray back, about 1-5/8" apart on center. (Scrape paint from the tray back, lay down beads of hot glue, and position the foam strips.) The foam acts as a spring to help hold the completed mirror firmly in place.
Clean mirror with a damp microfiber cloth—no abrasive or chemical sprays.
The slight mirror convexity makes reflected objects appear a bit smaller and farther away, but you'll quickly become accustomed. The curvature also reduces headlight glare from following night traffic by scattering the light.
Allow time to trust your new mirror. Nervous head-swiveling is a hard habit to break. But consider that whenever you've been looking backward in traffic, you've been risking sudden danger to the front. All it would take for an accident would be a driver in front of you slamming on brakes, or for road debris to suddenly appear in your path while your head is turned. You'll find the wide-angle mirror easier and safer to use than continually looking backward.
It helps to set your outside mirrors to fully cover blind spots. For the left, lean over until your head touches the side window glass, then set the side mirror so the right edge of it just picks up your rear fender. Lean the same amount to set the right mirror. Now you'll have a combined quick rear view of nearly 180°, far more than any stock rearview combination allows. By the time a vehicle that is overtaking you in a lane to either side leaves your new mirror's field, you'll see it showing up in a side mirror.
Your new mirror has got your back.