Lenses and mirrors: convex, concave, and plane mirrors

Basics of Mirrors

1. A mirror is a reflective surface that forms images by reflecting light.
2. Plane mirrors produce upright, virtual images with the same size as the object.
3. Curved mirrors are classified as concave or convex based on the direction of curvature.

Concave Mirrors

1. A concave mirror has a reflective surface that curves inward.
2. It can produce real or virtual images depending on the object's position relative to the mirror's focal point.
3. Common uses include telescopes, headlights, and shaving mirrors.
4. The focal length of a concave mirror is positive, indicating that the focus lies in front of the mirror.
5. Images formed by concave mirrors are magnified or diminished, depending on the object distance.

Convex Mirrors

1. A convex mirror has a reflective surface that bulges outward.
2. It always produces a virtual, diminished, and upright image.
3. Convex mirrors are widely used in rear-view mirrors and security mirrors due to their wide field of view.
4. The focal length of a convex mirror is negative, as the focus lies behind the mirror.
5. Convex mirrors never form a real image because reflected rays diverge.

Plane Mirrors

1. A plane mirror has a flat reflective surface.
2. The image formed is virtual, erect, and of the same size as the object.
3. The distance of the image from the mirror is equal to the distance of the object from the mirror.
4. Plane mirrors do not produce image distortion, making them suitable for everyday use, like in bathrooms and dressing tables.

Reflection Laws and Applications

1. All mirrors obey the laws of reflection: the angle of incidence equals the angle of reflection.
2. The normal to the surface determines the incident and reflected angles.
3. Concave mirrors focus parallel rays of light to a single point, used in solar concentrators.
4. Convex mirrors diverge light rays, reducing image size, ideal for traffic intersections.

Key Formulas

1. The mirror equation: 1/f = 1/v + 1/u, where f is focal length, v is image distance, and u is object distance.
2. The magnification: m = h'/h = -v/u, where h' is image height and h is object height.

Image Characteristics

1. Real images are formed when light rays converge and can be projected on a screen.
2. Virtual images occur when light rays appear to diverge and cannot be projected.
3. Image size and nature vary with the object's position relative to the focus and center of curvature.

Applications in Optical Instruments

1. Microscopes and telescopes use mirrors and lenses to magnify images.
2. Periscopes and kaleidoscopes rely on plane mirrors for image reflection.
3. Convex mirrors are crucial in parking lots and road safety.
4. Concave mirrors are used in makeup mirrors and dentistry.