determine the index of refraction of the glass.

You have just installed a new bathroom in your home. Your shower doors have frosted glass to provide privacy for the person using the shower. The frosted surface is on the outside of the shower door, facing the rest of the bathroom. The frosting is done by acid etching the surface so that light incident on the rough surface is scattered in all directions. Proud of your new bathroom, you take a photo of it with your smartphone. You notice in the photograph that you can see a reflection of the flash in the shower doors and the reflection is surrounded by a halo of light. Curious, you turn on a laser pointer and aim it at the shower door. Looking closely at the reflection, you again see a halo that consists of a dark area surrounding the reflection of the pointer and then an area of brightness outside this dark ring. You grab a micrometer and a ruler and measure the thickness of the glass to be 6.35 mm and the inner radius of the bright halo to be 10.7 mm. From these measurements, you determine the index of refraction of the glass.