Understanding Image Formation by Convex Mirrors
This solution explains the characteristics of the image formed by a convex mirror when a real object is placed in front of it. We will analyze the nature (real or virtual), orientation (erect or inverted), and position of the image.
Nature of Convex Mirrors
A convex mirror is a diverging mirror. This means parallel rays of light falling on it diverge after reflection, appearing to come from a point behind the mirror.
Image Characteristics with a Real Object
When a real object is placed in front of a convex mirror, regardless of its position (whether far away or close), the image formed always has the following characteristics:
- Nature: The image is always virtual. A virtual image is formed where light rays only appear to converge, and it cannot be projected onto a screen. It is formed behind the mirror.
- Orientation: The image is always erect (upright), meaning it has the same orientation as the object.
- Size: The image is always diminished, meaning it is smaller than the object.
- Position: The image is always located behind the mirror, specifically between the pole (P) and the principal focus (F).
Analysis of Options
Let's examine each option based on the known properties of image formation by convex mirrors:
| Option | Description | Analysis |
|---|---|---|
| 1 | The image is always real, inverted, and located between the principal focus and the center of curvature. | This is incorrect. Convex mirrors form virtual and erect images for real objects, not real and inverted ones. |
| 2 | The image is always virtual, erect, and located between the principal focus and the pole, behind the mirror. | This matches the characteristics of an image formed by a convex mirror with a real object. The image is virtual, erect, diminished, and located between P and F behind the mirror. |
| 3 | The image is always virtual, inverted, and located beyond the principal focus, behind the mirror. | This is incorrect. While the image is virtual and behind the mirror, it is always erect, not inverted. |
| 4 | The image can be real or virtual, depending on the object's distance from the mirror, and is always magnified. | This is incorrect. The image formed by a convex mirror with a real object is *always* virtual, never real. It is also always diminished (smaller), not magnified. |
| 5 | (No text provided for option 5) | This option cannot be evaluated. |
Conclusion
Based on the analysis, the statement that correctly describes the image formed by a convex mirror with a real object is that the image is always virtual, erect, and located between the principal focus (F) and the pole (P), behind the mirror.
Important Questions from Mirrors and Images
- A beam of parallel light, originating from a distant source, is first incident on a convex lens with focal length $f_2$.
Subsequently, the light passes through the lens and then reflects from a concave mirror having a focal length $f_1$.
The concave mirror is placed at a distance $d$ from the convex lens.
For the light rays to retrace their original path and ultimately emerge from the lens as a parallel beam heading back towards the distant source, the separation distance $d$ between the lens and the mirror must be: The total number of images formed by two mirrors inclined at 72° to each other when the object is placed unsymmetrically will be ___?
A short linear object of length b lies along the axis of a concave mirror of focal length f at a distance u from the pole of the mirror. The size of the image is ;
- A concave mirror of focal length $f$ produces an image $n$ times the size of the object. If the image is virtual, then the distance of the object from the mirror is:
- A concave mirror forms a real and inverted image of a distant object at a distance of $15 \text{ cm}$ from the mirror.
If an object is placed $20 \text{ cm}$ in front of this mirror, what will be the nature and magnification of the image formed?
