Understanding Why Convex Mirrors and Concave Lenses Cannot Produce Real Images

To understand why a convex mirror and a concave lens can never produce a real image, we need to delve into how these optical devices interact with light. This article breaks down the key concepts and provides a comprehensive explanation.

Convex Mirror

Shape and Reflection

A convex mirror is curved outward. When parallel rays of light strike the surface of a convex mirror, they are reflected outward. The reflection of light follows the laws of reflection, leading to the formation of a diverging beam of light.

Virtual Image Formation

The reflected light rays, although appearing to diverge from a common point behind the mirror, do not actually converge at any real point. This point is known as the virtual image. Since the light rays do not actually intersect, a real image cannot be produced. Instead, the image formed by a convex mirror is always virtual, upright, and reduced in size.

Image Characteristics

The image characteristics of a convex mirror are as follows:

Virtual Upright Reduced in size

Concave Lens

Shape and Refraction

A concave lens is thinner at the center and thicker at the edges. When parallel rays of light pass through a concave lens, they are refracted outward, leading to divergence of the light rays.

Virtual Image Formation

The refracted rays appear to diverge from a common point on the same side of the lens as the object. This divergence of light rays leads to the formation of a virtual image. The virtual image produced by a concave lens is always virtual, upright, and smaller than the object.

Image Characteristics

The characteristics of the image formed by a concave lens are:

Virtual Upright Smaller in size

Summary

The primary reason why a convex mirror and a concave lens cannot produce a real image is that they cause light rays to diverge. A real image requires the light rays to converge at a point. In the case of a convex mirror and a concave lens, the light rays do not actually converge, resulting in the formation of a virtual image.

Exception: Cassegrain Telescopes

There are exceptional cases where a convex mirror can form a real image. This occurs when the object being observed forms a virtual image behind the mirror. Consider the following scenario:

Light rays are converging and are focused by a primary mirror to a virtual focus. The virtual focus is located behind the convex mirror. The convex mirror is positioned such that the distance from the mirror vertex to the virtual focus is greater than half the radius of curvature. In this configuration, the convex mirror redirects the wavefront and forms a real image in front of it.

However, this scenario is rare and specific to particular setups, such as in Cassegrain telescopes. In a typical scenario, the convex mirror interacts with collimated light, which does not have the correct curvature to form a real image.

The difference between a concave and convex mirror is illustrated in the figures below:

Cassegrain Telescope Example

The figure below shows a ray diagram of a Cassegrain telescope, highlighting how the convex mirror can form a real image:

As you can see in the diagram, the convex mirror in a Cassegrain telescope correctly converges the light rays to form a real image, which is typically located at the secondary mirror or eyepiece.

Therefore, it is not as straightforward as simply stating that convex mirrors and concave lenses cannot produce real images. The ability to form a real image depends on the shape of the wavefront and the specific setup of the optical device. If the wavefront is planar or diverging, a real image will not form. If the wavefront is converging, then a real image can be formed, as seen in unique setups like Cassegrain telescopes.