Question

You have made a simple telescope from two convex lenses. The objective lens is the one of the two lenses that is closer to the object being observed. What kind of image is produced by the eyepiece lens if the eyepiece is closer to the objective lens than the image produced by the objective lens?

Short answer

Answer: The eyepiece lens produces a virtual, right-side-up, and enlarged image when it is closer to the objective lens than the image produced by the objective lens.

Step-by-step solution

Understand the simple telescope structure and ray paths

A simple telescope consists of two convex lenses, the objective lens, and the eyepiece lens. The objective lens is closer to the object being observed and has the role of forming the first image. The eyepiece lens acts as a magnifier for the first image, enabling the observer to see a larger image of the object.

Identify ray paths through the objective lens

As light rays from the object pass through the objective lens, they are refracted and converge at the focal point. The distance between the lens and the focal point is called the focal length (f). Beyond the focal length (between f and 2f), the light rays converge, and a real inverted image is formed.

Determine the position of the eyepiece lens

The eyepiece lens should be closer to the objective lens than the image produced by the objective lens. This means the eyepiece lens should intercept the converging light rays before they form a real image, i.e., between f and 2f of the objective lens.

Determine the ray paths through the eyepiece lens and the type of image formed

As the converging rays from the objective lens pass through the eyepiece lens, they are refracted again. Since the eyepiece lens is placed between f and 2f of the objective lens, it intercepts the converging light rays before they can form a real image. Hence, the rays will appear to be diverging from a point behind the eyepiece lens, creating a virtual, right-side-up, and enlarged image. So the type of image produced by the eyepiece lens when the eyepiece is closer to the objective lens than the image produced by the objective lens is a virtual, right-side-up, and enlarged image.

Key concepts

Convex Lenses

Convex lenses, often referred to as converging lenses, have a shape where the center is thicker than the edges. Imagine holding a spoon, the front part of which bulges outward; it has a similar shape to a convex lens. Such lenses are fundamental in multiple optical devices, including telescopes and glasses.

When light rays enter a convex lens, they are bent inwards towards a point known as the focal point. This bending occurs because the speed of light changes as it moves from air into the denser lens material. Convex lenses are useful for focusing light and forming images, which can be real or virtual depending on the position of the object relative to the lens.

Focal Length

Focal length is a critical concept in the study of optics—it's the distance from the center of a lens to the point where parallel rays of light converge or appear to diverge after passing through the lens. This point is called the focal point. For convex lenses, the focal length is a positive value and determines the strength of the lens: the shorter the focal length, the more powerful the lens, and the more it bends the light.

In practical terms, the focal length influences how a lens magnifies distant objects. In telescopes, for example, a lens with a large focal length can bring far-away stars or planets into clear, close-up view.

Ray Paths

Understanding ray paths through lenses is essential to grasp how images are formed. In a simple telescope, there are two main sets of ray paths to consider: those through the objective lens and those through the eyepiece lens.

Light from an object follows straight paths until it interacts with a lens. In our telescope example, the rays first encounter the objective lens. Depending on their initial angle, they are bent and may converge to form a real image. The location where this image forms depends on the object's distance and the lens's focal length. When this converging light then goes through the eyepiece, the final image is formed based on how these rays are refracted once more.

Virtual Image

A virtual image is an optical phenomenon that occurs when diverging light rays from an object appear to originate from a particular location, even though they don't actually converge there. Unlike a real image, a virtual image cannot be projected onto a screen because the light rays don't actually come together in real space.

In telescopes, the eyepiece lens creates a virtual image. By positioning the eyepiece lens in such a way that it intercepts the rays before they focus, it causes them to diverge. This results in an image that seems to be located on the same side of the lens as the viewer, providing an enlarged, upright, and more comfortable viewing experience. The virtual image is where the extended light rays from the lens appear to meet when traced back by our eyes or by a camera, allowing us to see a clear picture of the distant sight.