Light — Reflection & Refraction — 50 Q&A

Light is a form of energy that travels in straight lines (in homogeneous media), undergoes reflection and refraction at boundaries, and shows behaviour like dispersion. In this chapter we treat light as rays for geometric optics.

1. The incident ray, reflected ray and normal at the point of incidence lie in the same plane.
2. Angle of incidence = angle of reflection (measured from normal).

Regular reflection: from smooth surfaces (plane mirror) producing clear images. Diffuse reflection: from rough surfaces scattering light in many directions (e.g., paper) — no clear image.

• Image is virtual (cannot be projected), erect, laterally inverted, same size as object.
• Image distance = object distance (measured from mirror).

Draw two rays from a point on the object: (a) one incident ray parallel to mirror, reflect back at same angle; (b) one incident ray at angle to normal. Extend reflected rays backward to meet — intersection is virtual image point.

P = pole (mirror midpoint). C = centre of the sphere from which mirror is a part. R = distance PC. Principal axis = line PC. F = focal point (where parallel rays converge for concave) at distance f = R/2 from pole.

Mirror formula: 1/f = 1/v + 1/u. Magnification: m = h'/h = -v/u. Use sign convention: object distance u negative (for real object in front), v negative for real image (concave), f negative for convex mirror (or follow your chosen convention consistently).

1. Beyond C: real, inverted, diminished, image between C & F.
2. At C: real, inverted, same size at C.
3. Between C & F: real, inverted, enlarged, beyond C.
4. At F: image at infinity (rays parallel).
5. Between F & P: virtual, erect, enlarged behind mirror.

Convex mirror always forms virtual, erect, diminished images located behind the mirror. Focal length is considered negative for convex mirror in sign convention.

Refraction is bending of light when it passes from one medium to another due to change in speed. Snell's law: n1 sin i = n2 sin r. Refractive index (n) = speed of light in vacuum / speed in medium, or ratio of sines for two media.

Absolute refractive index (n) = c / v (v = speed in medium). Relative refractive index of medium2 w.r.t medium1 = n2/n1. Typical: air ≈ 1.00, water ≈ 1.33, crown glass ≈ 1.5.

When light enters and exits a parallel-sided slab it emerges parallel to the incident ray but shifted laterally. Shift depends on slab thickness, angle of incidence and refractive index.

Refraction at spherical surface: (n2/v) - (n1/u) = (n2 - n1)/R, with sign conventions. This is used to locate images by refracting surfaces and lenses.

Thin lens formula: 1/f = 1/v - 1/u (or 1/f = 1/v + 1/u depending on sign convention). Lens-maker's formula: 1/f = (n-1)(1/R1 - 1/R2) for a lens in air (R1,R2 radii of curvature).

1. Object at infinity: image at focus F, highly diminished.
2. Beyond 2F: real, inverted, diminished (between F and 2F).
3. At 2F: real, inverted, same size at 2F.
4. Between F and 2F: real, inverted, enlarged, beyond 2F.
5. At F: image at infinity.
6. Closer than F: virtual, erect, enlarged on same side as object.

Concave lens always produces a virtual, erect, diminished image located on the same side as the object. Used in spectacles for myopia (short-sightedness) correction.

Magnification m = h'/h = -v/u for lenses (h' image height, h object height). Sign indicates inversion (negative for inverted image).

Power P = 1/f (f in meters). Unit is dioptre (D). A convex lens has positive power; concave has negative power.

For lenses in contact: 1/f = 1/f1 + 1/f2. Powers add: P = P1 + P2 (P in dioptres).

Dispersion: splitting of white light into constituent colours due to wavelength-dependent refractive index — shorter wavelengths (violet) refract more than longer (red).

Sunlight enters raindrop → refracts & disperses → internal reflection → refracts again leaving drop. Different colours exit at different angles; observer sees circular spectrum (rainbow).

Apparent depth is the perceived depth of an object submerged in a medium (e.g., coin in water) which appears shallower. For normal viewing: apparent depth = real depth / n approximately.

Spherical aberration and chromatic aberration. Reduce by using stops (small aperture), aspheric surfaces or achromatic doublets (combining glasses with different dispersion).

Real image: rays actually converge and can be projected on a screen (e.g., image by concave mirror when object beyond F). Virtual image: rays only appear to diverge from image point and cannot be projected (e.g., plane mirror image).

Minimum deviation occurs when the path inside prism is symmetrical. n = sin((A + D_min)/2) / sin(A/2), where A is prism angle and D_min is minimum deviation.

Use 1/f = 1/v + 1/u. With f = −15 cm (concave), v = −10 cm (real image): 1/−15 = 1/−10 + 1/u ⇒ 1/u = 1/−15 − 1/−10 = (−2 + 3)/30 = 1/30 ⇒ u = 30 cm. Magnification m = −v/u = −(−10)/30 = 1/3 (image one-third size, inverted).

Light from coin refracts at water-air surface towards observer, bending away from normal — rays enter eye as if coming from a point closer to surface (apparent depth less than real depth).

Atmospheric refraction: rays from lower limb of Sun bend more (denser air near surface) than upper limb, making the Sun appear flattened vertically. Scattering reddens colour too.

Atmospheric refraction shifts apparent positions of celestial objects upward (near horizon effect is largest), causing stars to be visible slightly before rising and after setting.

Primary rainbow: light refracts, internally reflects once, then refracts out. Secondary: two internal reflections — so emerges at larger angles, undergoes more loss (fainter) and colour order is reversed.

Myopia (short-sighted): use concave (diverging) lenses to move image onto retina. Hypermetropia (long-sighted): use convex (converging) lenses to form image on retina.

At any boundary between different refractive indices, part of light is reflected and part refracted. Reflectance depends on refractive index contrast and angle (Fresnel equations) — qualitatively larger contrast → more reflection.

Two plane mirrors inclined at 45° reflect light from object into observer's eye, allowing view over obstacles.

Lenses focus light to form a real inverted image on the film/sensor. Aperture controls light amount and depth of field; focusing adjusts lens-sensor distance to get sharp image.

Accommodation: change in focal length of eye's lens by ciliary muscles — lens becomes thicker for near vision and thinner for distant vision to focus images on retina.

Mirages are due to refraction in air layers with varying density (temperature gradient). Light bends and may undergo total internal reflection within hot layers, producing illusion of water/reflected sky.

Point mirror at a distant object (sun or far building) so object is effectively at infinity. Measure distance from mirror pole to sharp image on screen — this ≈ focal length.

Prisms fold optical path, correct image orientation (erect the inverted image from objective lens) and enable a compact binocular design while maintaining magnification.

Prescription lists lens power in dioptres (D): negative for diverging (myopia), positive for converging (hypermetropia). E.g., −2 D lens has focal length −0.5 m (1/−2).

In a medium, electromagnetic waves interact with atoms/molecules, causing induced dipoles and re-emission leading to an effective reduced phase velocity; refractive index quantifies this reduction.

With age, lens loses elasticity and ciliary muscles weaken; lens cannot become sufficiently convex for near vision, causing presbyopia — corrected by reading glasses (convex lenses).

Geometric optics ignores wave phenomena (diffraction, interference, polarization). It works when object sizes and apertures are much larger than wavelength of light.

1. Use distant object (sun) and measure image distance ≈ focal length.
2. Use object-lens-screen, measure u and v and apply lens formula 1/f = 1/v - 1/u.

Magnifying power depends on focal lengths of objective and eyepiece: typically ratio f_obj / f_eye for astronomical telescope in normal adjustment — larger objective focal length and smaller eyepiece focal length give higher magnification.

• Mirror: 1/f = 1/v + 1/u.
• Thin lens: 1/f = 1/v - 1/u (signs per convention).
• Snell's law: n1 sin i = n2 sin r.
• Critical angle: sin θc = n2 / n1 (n1>n2).
• Magnification: m = -v/u = h'/h.
• Power: P = 1/f (m).