If objects seen in a vehicle rear-view mirror appear enlarged and inverted, which type of mirror is being used?

Introduction / Context:
In geometrical optics, different types of mirrors form images with very specific characteristics. Plane mirrors form images of the same size, convex mirrors form diminished upright images, and concave mirrors can form magnified or diminished images that may be upright or inverted depending on the position of the object. This question asks you to connect the observed properties of the image in a rear-view mirror enlarged and inverted with the correct type of mirror.

Given Data / Assumptions:

• The mirror is being used as a rear-view mirror in some vehicle or setup.
• The objects seen in the mirror appear enlarged compared with their actual size.
• The images are inverted (upside down) relative to the objects.
• We assume ideal mirrors and use standard sign conventions from school level optics.

Concept / Approach:
The key idea is that image properties size and orientation depend on mirror type and object position. A concave mirror can produce three main kinds of images: real inverted and magnified (object between centre of curvature C and focus F), real inverted and diminished (object beyond C), or virtual upright and magnified (object between focus F and mirror). Convex mirrors, by contrast, always give virtual, upright and diminished images. Plane mirrors always give virtual, upright images of the same size as the object. Therefore, enlarged and inverted immediately points toward a concave mirror with the object between C and F.

Step-by-Step Solution:
Step 1: Note that the image is enlarged, so the magnification is greater than one in magnitude. Step 2: Note that the image is inverted, meaning it is upside down relative to the object. Step 3: Recall that convex mirrors never produce inverted images; they always produce diminished upright images. Step 4: Recall that plane mirrors produce images of the same size and always upright. Step 5: Recognise that only concave mirrors can produce magnified inverted images when the object is placed between the centre of curvature and the focus. Step 6: Conclude that the mirror must be a concave mirror.

Verification / Alternative check:
Ray diagram construction for a concave mirror with the object between C and F shows rays converging to form a real image beyond C. The image is larger than the object and inverted. A quick comparison with ray diagrams for plane and convex mirrors confirms that those combinations never produce this enlarged inverted real image. Thus, concave mirrors are uniquely capable of matching the description given in the question.

Why Other Options Are Wrong:
Convex mirror: Always forms virtual, upright and diminished images, suitable for normal rear-view mirrors but not for enlarged inverted images.

Cylindrical mirror: Used in special optical instruments, but the basic school level classification focuses on plane, concave and convex; cylindrical curvature alone does not specifically give the enlarged inverted rear-view effect described.

Plane mirror: Always gives an image of the same size as the object and upright, so it cannot produce an enlarged inverted image.

Common Pitfalls:
Students sometimes memorise that rear-view mirrors in cars are convex and then mechanically choose convex even when the question explicitly describes image properties that do not match a convex mirror. The safe approach is to focus on the image characteristics given magnified and inverted and match those to the correct mirror type using ray diagrams and basic mirror formulas, rather than relying only on the word rear-view.

Final Answer:
A rear-view mirror that shows enlarged, inverted images must be a concave mirror.