(b) An object is set 20 cm in front of a lens, and a real, inverted, magnified image is formed at a great distance. State the type of lens used and determine the value of the focal length.
Answer (2)
Identify the lens type as convex due to the real, inverted, and magnified image.
Recognize that a real image at a great distance implies the object is at the focal point.
Equate the focal length to the object distance: f = ∣ u ∣ .
Determine the focal length: 20 cm .
Explanation
Problem Analysis Let's analyze the problem. We are given that an object is placed 20 cm in front of a lens, and a real, inverted, magnified image is formed at a great distance. We need to determine the type of lens and its focal length.
Type of Lens Since the image is real, inverted, and magnified, the lens must be a convex lens (also known as a converging lens). Convex lenses can form real and inverted images when the object is placed outside the focal length.
Image at Infinity The problem states that the image is formed at a great distance, which we can approximate as infinity. This occurs when the object is placed at the focal point of the lens. Therefore, the object distance is equal to the focal length.
Focal Length Calculation Given that the object distance u = 20 cm, and since the object is placed in front of the lens, we use the sign convention where u is negative. Thus, u = − 20 cm. However, the focal length f is a positive value for a convex lens. Since the object is at the focal point, the focal length is equal to the absolute value of the object distance: f = ∣ u ∣ = ∣ − 20∣ = 20 cm.
Final Answer Therefore, the lens is a convex lens, and its focal length is 20 cm.
Examples
Understanding lenses is crucial in various applications, such as designing eyeglasses, telescopes, and cameras. For instance, if you're designing a simple telescope and need a magnified image of a distant object, you'd use a convex lens. Knowing the focal length helps you position the lenses correctly to achieve the desired magnification and image clarity. In this case, a lens with a 20 cm focal length would be suitable for creating an initial magnified image.
The lens used is a convex lens, and the focal length is 20 cm. This is determined because a real, inverted, magnified image is formed at a great distance when the object is at the focal point. Therefore, the focal length matches the object distance of 20 cm.
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