Bonding a piece of acrylic to a piece of glass is rather difficult because acrylic is synthetic whereas glass is not. This means that each material requires a different type of adhesive in order to bond to anything. Unfortunately, no particular adhesive is quite as effective with both acrylic and glass as some adhesives are with just one of the materials. In order to glue acrylic to glass, you will want to install a bulkhead to provide the greatest part of the pressure keeping the materials together, with the glue acting as a sealant.
Things You'll Need
Sand the acrylic surface you'll be bonding to the glass. In order for the glue to be at all effective, the surface will need to be as flat as possible. According to Ozreef.com, 240-gauge sandpaper is appropriate for achieving a sufficiently fine surface. As for sanding uniformly, try taping the sandpaper to another flat object and sanding the acrylic steadily and firmly.
Drill the holes where you will eventually insert the bulkheads. Match up all the pieces into the final form and mark where the bulkhead will eventually sit. According to Fins.actwin.com, use a drill bit specifically designed for acrylic on the acrylic. Northcoastmarines.com advises using a variable speed drill on the glass to allow you to speed up gradually to avoid shattering the glass.
Clean both the acrylic and glass surfaces with isopropyl alcohol. Extrinsic substances such as skin oils or debris from the sanding and drilling can interfere with the adhesive's effectiveness and ruin your project. Thoroughly clean all surfaces that will be glued and avoid touching them again.
Glue the pieces together. Follow the application instructions on your adhesive and allow the necessary dry time. Most glue will not require too much to be used in order to be effective. A suggested adhesive is epoxy, such as Bostik Titan Bond Plus.
Install the bulkheads for which you drilled holes. Again, be mindful of glass's brittleness and use a variable speed drill. A lubricant may be necessary: check with the bulkheads' packaging and manufacturer's instructions. Always wait until the glue is absolutely dry before installing the bulkheads.
Acrylic glues are toxic and very dangerous. Only work in a well-ventilated area and avoid inhaling fumes and contacting the skin.
Do not drill tempered glass. It will shatter.