The Mermaid's Purse is not an invertebrate at all - it is a fish egg capsule. The egg capsule of a skate or ray, to be precise. The "horns" are to secure the capsule in seaweed. You may find one with a baby skate growing inside, but most are empty. They are included here with bivalves because they are often found scattered around the bottom like shells, up to 3" long. They certainly don't look like fish!
When light travels from a less-dense medium like air to a more-dense medium like water, the rays are refracted or bent towards the normal or perpendicular of the surface between the two mediums. In crude terms, light going from air to water will tend to be straightened, while light going from water to air will tend to be ... um ... crookeded. Confused yet? Take a look at the figure below.
In this figure, you can see the light rays traveling from an object in the water to your eyes, neglecting the effect of the flat glass lens of your mask. The blue lines trace the actual path of the light rays through the water and into the air, or conversely, through the air into the water - the direction really doesn't matter. As you can see, the rays are bent toward the perpendicular of the surface on the water side, and away from it on the air side.