Where should an object be placed in front of a convex lens to get a real and enlarged image of the object ?
Between the principal focus and twice the focal length
Understanding Image Formation by a Convex Lens
A convex lens can form different types of images depending on where the object is placed in front of it. We are looking for the specific object position that results in a real and enlarged image.
Image Characteristics for Different Object Positions with a Convex Lens
Let's analyze the image formed when the object is placed at various positions relative to the principal focus (F) and twice the focal length (2F) of a convex lens. We'll denote the focal length as \(f\).
- Object at Infinity: The image is formed at the principal focus (\(F\)). The image is real, inverted, and highly diminished (a point image).
- Object Beyond \(2F\): The image is formed between \(F\) and \(2F\). The image is real, inverted, and diminished.
- Object at \(2F\): The image is formed at \(2F\). The image is real, inverted, and of the same size as the object.
- Object Between \(F\) and \(2F\): The image is formed beyond \(2F\). The image is real, inverted, and enlarged.
- Object at \(F\): The image is formed at infinity. The image is real, inverted, and highly enlarged.
- Object Between the Optical Centre (\(O\)) and \(F\): The image is formed on the same side of the lens as the object. The image is virtual, erect, and enlarged.
Finding the Object Position for Real and Enlarged Image
Based on the analysis above, the case that produces a real and enlarged image is when the object is placed between the principal focus (\(F\)) and twice the focal length (\(2F\)). In this situation, the light rays from the object converge after passing through the convex lens to form a real image on the other side, which is larger than the object and inverted.
Evaluating the Given Options
- At twice the focal length (\(2F\)): This position results in a real, inverted image of the same size. This is not an enlarged image.
- At infinity: This position results in a real, inverted, and highly diminished image (point size) at the focus. This is not an enlarged image.
- Between the principal focus and twice the focal length (Between \(F\) and \(2F\)): This position results in a real, inverted, and enlarged image formed beyond \(2F\). This matches the requirement for a real and enlarged image.
- Beyond twice the focal length (Beyond \(2F\)): This position results in a real, inverted, and diminished image formed between \(F\) and \(2F\). This is not an enlarged image.
Therefore, placing the object between the principal focus and twice the focal length in front of a convex lens produces a real and enlarged image.
Summary of Convex Lens Image Formation
| Object Position | Image Position | Nature of Image | Size of Image |
|---|---|---|---|
| At infinity | At \(F_2\) | Real and inverted | Highly diminished (point size) |
| Beyond \(2F_1\) | Between \(F_2\) and \(2F_2\) | Real and inverted | Diminished |
| At \(2F_1\) | At \(2F_2\) | Real and inverted | Same size |
| Between \(F_1\) and \(2F_1\) | Beyond \(2F_2\) | Real and inverted | Enlarged |
| At \(F_1\) | At infinity | Real and inverted | Highly enlarged |
| Between \(O\) and \(F_1\) | On the same side of the lens as the object | Virtual and erect | Enlarged |
Note: \(F_1\) and \(2F_1\) are on one side, and \(F_2\) and \(2F_2\) are on the other side of the lens. For a convex lens, we typically consider \(F_1\) and \(2F_1\) as the object side and \(F_2\) and \(2F_2\) as the image side for real images.
Revision Table: Convex Lens Image Characteristics
| Object Location | Image Properties |
|---|---|
| Very far (infinity) | Real, Inverted, Very Small (at focus) |
| Far (Beyond 2F) | Real, Inverted, Small (between F and 2F) |
| Medium (At 2F) | Real, Inverted, Same Size (at 2F) |
| Near (Between F and 2F) | Real, Inverted, Large (Beyond 2F) |
| Very Near (At F) | Real, Inverted, Very Large (at infinity) |
| Extremely Near (Between O and F) | Virtual, Erect, Large (on object side) |
Additional Information on Convex Lenses and Images
A convex lens is also known as a converging lens because it converges parallel rays of light to a single point (the principal focus) after refraction. It is thicker in the middle and thinner at the edges. Convex lenses are used in various optical instruments like cameras, projectors, magnifying glasses, and telescopes.
Understanding the relationship between object distance, image distance, and focal length is crucial. This relationship is described by the lens formula:
\[\frac{1}{v} - \frac{1}{u} = \frac{1}{f}\]
where:
- \(v\) is the image distance from the optical centre.
- \(u\) is the object distance from the optical centre.
- \(f\) is the focal length of the lens.
The magnification (\(m\)) produced by a lens is given by:
\[m = \frac{\text{Height of image}}{\text{Height of object}} = \frac{v}{u}\]
For a real image, \(v\) is positive, and for a virtual image, \(v\) is negative. For an inverted image, magnification \(m\) is negative, and for an erect image, \(m\) is positive. An enlarged image has \(|m| > 1\).
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