Final answer:
Half-cylindrical lenses are used in critical angle experiments to demonstrate that perfect images can be formed through total internal reflection, even with only half a lens. This is especially useful in applications like binoculars and periscopes, where cost-effective and versatile design is important.
Step-by-step explanation:
Half-cylindrical lenses are used in critical angle experiments because they are efficient in demonstrating total internal reflection. When total internal reflection occurs, conditions are such that the critical angle is less than 45°, which is easily achieved with common materials. These lenses are practical because they show that you don't need an entire lens to form an image; half a lens will suffice, creating an albeit fainter image. This concept is mirrored in devices like binoculars and periscopes, where corner reflectors operate under the principle of total internal reflection to provide perfect mirror-like reflection.
In essence, although we might assume that the entire lens is needed to project an image, using just half of the lens can also project the same image. This understanding is crucial in optics, especially when considering the manufacture of lenses and their cost-effectiveness. Knowing that a complete lens is not always necessary allows for more versatile designs and applications, such as in periscopes in submarines and the internal mirrors within binoculars.