Plano-convex lens with its convex side silvered , then why it is a combination of two plano-convex lens and a concave mirror?

When we talk about a plano-convex lens that has its convex side silvered, we are essentially transforming it into a unique optical device that combines the properties of both a lens and a mirror. This setup can be understood by examining how light interacts with the different surfaces of the lens and the mirror.

Understanding the Structure

A plano-convex lens has one flat (plano) side and one outwardly curved (convex) side. When the convex side is coated with a reflective material, it behaves like a concave mirror. This means that light entering the lens will first pass through the plano side, then reflect off the silvered convex side.

How Light Interacts

Let’s break down the interaction of light with this combination:

• Incident Light: When parallel rays of light hit the plano side, they pass through the lens and converge towards a focal point due to the lens's curvature.
• Reflection: After passing through, these rays hit the silvered convex surface. Instead of continuing onward, they reflect back towards the plano side.
• Re-focusing: As the reflected rays travel back through the lens, they are refracted again, effectively behaving as if they are passing through a second plano-convex lens.

Combining Optical Properties

This unique configuration can be thought of as two plano-convex lenses working in tandem with a concave mirror. Here’s why:

• First Lens Effect: The initial passage through the plano side acts like a plano-convex lens, converging the light.
• Mirror Effect: The silvered convex side reflects the light, similar to how a concave mirror would redirect light rays.
• Second Lens Effect: The returning light passes through the plano side again, refracting and converging once more, akin to a second plano-convex lens.

Practical Applications

This combination is particularly useful in optical devices such as laser systems and certain types of telescopes, where precise control over light paths is essential. The ability to manipulate light through both refraction and reflection allows for more compact designs and enhanced performance.

Visualizing the Concept

Think of it like a two-step process where light first gets focused by the lens, then redirected by the mirror, and finally refocused again by the lens. This dual action maximizes the efficiency of light manipulation, making it a clever design in optics.

In summary, a plano-convex lens with its convex side silvered acts as a combination of two plano-convex lenses and a concave mirror due to the way it refracts and reflects light. This innovative design allows for enhanced optical performance in various applications.