If you place a paper clip below a beaker and pour water into the beaker why can't the paper clip be seen from the side of the beaker?

This phenomenon is due to the principles of refraction and total internal reflection. Refraction is the cause of heat haze, and of the dappled light at the bottom of a shallow pool. It helps makes diamonds sparkle and plays a part in rainbows.

What your expirement demonstrates are the principles of refraction and total internal reflection. In explaination, the light from the paper clip is being refracted as it enters the bottom of the beaker. When it hits the side of the beaker it strikes at such an angle that it undergoes total internal reflection and can only exit the water at the top surface.

The paper clip seems to disappear! This is really the principle of fiber optics. Light enters one end of the fiber and can only exit at the other end.