Question

Lens and mirror

Answer 1

Do you want a quick overview, the physics and equations, or worked examples/diagrams? Below is a concise but complete primer on lenses and mirrors — types, ray rules, image formation, and the key formulas.

What they are
- Lens: transparent object that refracts (bends) light to form images. A thin lens has two refracting surfaces.
- Converging (convex) lens: brings parallel rays to a focus (positive focal length).
- Diverging (concave) lens: spreads parallel rays as if from a virtual focus (negative focal length).
- Mirror: reflective surface that redirects light.
- Concave (spherical) mirror: reflective surface curves inward; it can converge rays (positive focal length).
- Convex (spherical) mirror: reflective surface bulges outward; it diverges rays (negative focal length).
- Plane mirror: flat, produces virtual images same distance behind the mirror.

Key ray rules (for constructing images)
- Thin lens (thin approximation):
1. Ray parallel to the principal axis → refracts through the focal point on the other side.
2. Ray through the center of the lens → continues undeviated.
3. Ray through the focal point on the object side → emerges parallel to the axis.
- Spherical mirror:
1. Ray parallel to axis → reflects through the focal point.
2. Ray through the center of curvature → reflects back on itself.
3. Ray through the focal point → reflects parallel to axis.

Basic equations
- Thin lens equation (both converging and diverging): 1/f = 1/do + 1/di
- f = focal length, do = object distance, di = image distance (use sign convention).
- Mirror equation (spherical mirror): 1/f = 1/do + 1/di (same algebraic form).
- Magnification (linear): m = hi/ho = -di/do
- hi = image height, ho = object height. Sign indicates orientation (negative = inverted).
- Lens-maker’s equation (thick/curved surfaces, for a thin lens in air):
1/f = (n − 1)(1/R1 − 1/R2)
- n = refractive index of lens material, R1 and R2 are radii of curvature (with sign convention).
- Focal length of a spherical mirror: f = R/2 (R = radius of curvature).

Sign conventions (common Cartesian sign convention)
- Distances measured from the optical vertex toward the incident light are positive for objects; use consistent convention: typically
- Object distance do > 0 if object is on the incoming-light side.
- Image distance di > 0 if image is on the outgoing side for lenses (real image), for mirrors di > 0 if image is in front of the mirror (real).
- Focal length f > 0 for converging elements, f < 0 for diverging.
(Be explicit about which convention you use when solving problems.)

Typical image cases for converging lens / concave mirror
- Object beyond 2f (or beyond R for mirrors): image is real, inverted, and smaller (between f and 2f).
- Object at 2f: image real, inverted, same size, at 2f.
- Object between f and 2f: image real, inverted, larger (beyond 2f).
- Object at f: image at infinity (rays become parallel).
- Object inside f: image virtual, upright, larger (on same side as object for lenses; behind mirror for convex).

Examples of uses
- Lenses: eyeglasses, cameras, microscopes, telescopes, magnifiers.
- Mirrors: shaving/makeup mirrors (concave), rearview mirrors (convex), telescopes, periscopes.

If you want:
- A worked numerical example (solve for di and magnification),
- Ray-diagram sketches,
- Sign-convention walkthrough,
say which and I’ll produce it.