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A real image is created when light rays actually converge at a point after passing through a lens. Unlike a virtual image, a real image can be captured on a screen because the light physically reaches that point. You find real images commonly in projectors and cameras.
A key distinction of real images is that they are always formed on the opposite side of the lens from the object. This occurs when the object is placed outside the focal point of a converging lens. Real images are typically inverted compared to the object.
In the context of this exercise, the lens forms a real image 214 cm away from the object, indicating a genuine convergence of light rays.

Converging lenses, also known as convex lenses, have a shape that bulges outward. These lenses focus incoming parallel light rays to a point known as the focal point. This property makes them indispensable in applications like magnifying glasses and eyeglasses for farsightedness.

• Converging lenses can form both real and virtual images based on the object's position relative to the focal point.
• When an object is beyond the focal length, they produce real and inverted images.
• If the object is placed within the focal length, a virtual and magnified image appears.

In our exercise, the lens is identified as a converging lens as it forms a real image and magnifies the object.

Magnification is the factor by which an image's size changes relative to the object. It is determined by the formula:\[m = \frac{-v}{u}\]where \(m\) is the magnification, \(v\) is the image distance, and \(u\) is the object distance.
A magnification value greater than one means the image is larger than the object, while a magnification less than one indicates a smaller image. Negative magnification denotes that the image is inverted compared to the object.
For this scenario, the image is \(1\frac{2}{3}\) times larger than the object, indicating a magnification of \(\frac{5}{3}\). This positive value means the image is bigger and is located on the opposite side of the lens from the object. As calculated in the solution, this aligns with the behavior of real images produced by converging lenses.

The focal length of a lens is the distance from the lens to its focal point. It determines how strongly the lens converges or diverges light. The formula to find the focal length using object and image distances is given by the lens equation:\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]where \(f\) is the focal length, \(v\) is the image distance, and \(u\) is the object distance.
For converging lenses, the focal length is positive, indicating that they focus light. In our exercise, applying the lens formula with \(v = -214\) cm and \(u = -128.4\) cm allows us to solve for \(f\). This computation yields a focal length demonstrating the lens's capability to focus light into a real image.