Light and Optics

Electromagnetic Spectrum

The electromagnetic (EM) spectrum arranges all EM radiation by wavelength λ and frequency f, related by c = fλ where c = 3.00 × 10⁸ m/s in vacuum. EM waves are transverse oscillations of perpendicular electric and magnetic fields; they require no medium and all travel at c in vacuum. The spectrum, from longest to shortest wavelength: radio waves (> 0.1 m), microwaves (1 mm–0.1 m), infrared (700 nm–1 mm), visible light (380–700 nm), ultraviolet (10–400 nm), X-rays (0.01–10 nm), and gamma rays (< 0.01 nm). Energy per photon is E = hf = hc/λ, where h = 6.626 × 10⁻³⁴ J·s = 4.136 × 10⁻¹⁵ eV·s. Thus, shorter wavelength = higher frequency = higher photon energy — UV photons carry more energy than IR photons, which is why UV causes DNA damage. The visible spectrum spans red (~700 nm, lowest energy visible) to violet (~380 nm, highest energy visible), remembered as ROYGBIV. The MCAT commonly tests this ordering: radio < microwave < infrared < visible < UV < X-ray < gamma for both frequency and energy, with wavelength following the reverse order. A key MCAT connection: the photoelectric effect demonstrates that light's particle-like behavior (photons) dominates at higher frequencies — a photon must exceed the work function φ (hf > φ) to eject an electron, and any excess energy becomes the electron's kinetic energy (K_max = hf − φ). This contradicts the classical wave prediction that intensity alone should eject electrons — the frequency threshold is the telltale sign of photon quantization.

Reflection and Refraction

Reflection and refraction describe what happens when light encounters a boundary between two media. The law of reflection states that the angle of incidence equals the angle of reflection: θᵢ = θ_r, both measured from the normal (perpendicular) to the surface. Refraction is the bending of light as it passes from one medium to another due to a change in speed. The index of refraction n = c/v quantifies this: n ≥ 1, where n = 1 for vacuum and n ≈ 1.33 for water, n ≈ 1.5 for glass. When light enters a medium with higher n (slower speed), it bends toward the normal; when entering a lower n, it bends away from the normal. This is the qualitative basis of Snell's law. The frequency of light does NOT change when crossing a boundary — only wavelength and speed change (λ_n = λ_vacuum / n). This is a critical MCAT concept: color is determined by frequency, not wavelength, which is why a red object still looks red underwater even though the wavelength shortens. Partial reflection and refraction occur at every interface — some light reflects, some transmits. At normal incidence (θᵢ = 0°), no bending occurs regardless of index change. Dispersion occurs because n varies slightly with wavelength: shorter wavelengths (violet) bend more than longer ones (red) in glass, producing a spectrum — this is how prisms separate white light into colors and why rainbows form.

Snell's Law and Total Internal Reflection

Snell's law quantifies refraction: n₁ sin θ₁ = n₂ sin θ₂, where θ₁ and θ₂ are measured from the normal. As light moves from lower n to higher n, sin θ decreases, so θ decreases — light bends toward the normal. Conversely, from higher n to lower n, light bends away from the normal. Total internal reflection (TIR) occurs when light in a higher-index medium strikes a boundary with a lower-index medium at an angle greater than the critical angle θ_c. At θ_c, the refracted ray grazes the boundary (θ₂ = 90°), so Snell's law gives: n₁ sin θ_c = n₂ sin 90° ⇒ sin θ_c = n₂ / n₁, and θ_c = sin⁻¹(n₂/n₁). TIR requires: (1) light traveling from higher n to lower n, and (2) θᵢ > θ_c. At angles below θ_c, both refraction and partial reflection occur. At θᵢ = θ_c, the refracted ray skims the surface. At θᵢ > θ_c, no light is transmitted — 100% reflection. TIR powers fiber optics: glass fibers (core n ≈ 1.5, cladding n ≈ 1.4) trap light via TIR, enabling high-speed data transmission and medical endoscopy. Diamond's brilliance comes from its high n (≈2.42), giving a small critical angle (≈24°) — light entering a diamond undergoes many TIRs before exiting, creating sparkle. The MCAT frequently asks: given n₁ = 1.5 and n₂ = 1.0 (air), find θ_c. Answer: θ_c = sin⁻¹(1.0/1.5) = sin⁻¹(0.667) ≈ 42°. Light incident at angles greater than 42° from within the higher-index medium undergoes TIR. A common MCAT twist: as n₂ approaches n₁, θ_c approaches 90°, and TIR becomes harder to achieve. If n₂ exceeds n₁, TIR is impossible regardless of angle — light will always refract (though weakly at large angles).

Mirrors and Image Formation

Mirrors form images by reflection. The mirror equation is 1/f = 1/d₀ + 1/dᵢ, identical in form to the thin lens equation, where f is focal length, d₀ is object distance, and dᵢ is image distance. Sign convention: concave mirrors (converging) have positive f; convex mirrors (diverging) have negative f. Image distance dᵢ is positive for real images (on the same side as the object for mirrors — in front of the mirror), negative for virtual images (behind the mirror). Magnification: m = −dᵢ/d₀ = hᵢ/h₀, where negative m means an inverted image. Concave mirrors produce real, inverted images when d₀ > f, and virtual, upright, magnified images when d₀ < f (makeup mirror). At d₀ = f, no image forms (rays emerge parallel). At d₀ = 2f = R (center of curvature), the image is real, inverted, and same size. Convex mirrors ALWAYS produce virtual, upright, diminished images regardless of object distance — this is why they are used as store security mirrors and car side mirrors ('objects in mirror are closer than they appear'). The focal length of a spherical mirror is f = R/2, where R is the radius of curvature. Ray diagrams use three principal rays: (1) a ray parallel to the principal axis reflects through the focal point; (2) a ray through the focal point reflects parallel to the axis; (3) a ray through the center of curvature (C) reflects back along itself. The MCAT expects you to identify image characteristics (real/virtual, upright/inverted, magnified/diminished) from either the sign of dᵢ and m or from a ray diagram. Practice: for an object at d₀ = 3 cm in front of a concave mirror with f = 2 cm, 1/dᵢ = 1/2 − 1/3 = 1/6 ⇒ dᵢ = +6 cm (real), m = −6/3 = −2 (inverted, magnified 2×).

Lenses and the Thin Lens Equation

Lenses form images by refraction. The thin lens equation is 1/f = 1/d₀ + 1/dᵢ, where f is focal length. Sign convention: converging (convex) lenses have positive f; diverging (concave) lenses have negative f. For lenses, a real image forms on the opposite side of the lens from the object (dᵢ positive), and a virtual image forms on the same side as the object (dᵢ negative). Lens power is measured in diopters: P = 1/f (with f in meters). A converging lens has positive power; a diverging lens has negative power. The MCAT frequently tests power in the context of the eye. Magnification: m = −dᵢ/d₀ = hᵢ/h₀. Converging lens image properties by object distance: (1) d₀ > 2f → real, inverted, diminished; (2) d₀ = 2f → real, inverted, same size; (3) f < d₀ < 2f → real, inverted, magnified (projector); (4) d₀ = f → no image (rays emerge parallel); (5) d₀ < f → virtual, upright, magnified (magnifying glass). Diverging lenses ALWAYS produce virtual, upright, diminished images — identical to convex mirrors. Ray diagrams for lenses use three principal rays: (1) a ray parallel to the axis refracts through the focal point on the far side (converging) or appears to come from the focal point on the near side (diverging); (2) a ray through the center of the lens continues undeviated; (3) a ray toward the focal point on the near side (converging) or toward the focal point on the far side (diverging) refracts parallel. Example: a 4 cm tall object is placed 10 cm from a converging lens with f = 6 cm. 1/dᵢ = 1/6 − 1/10 = 1/15 ⇒ dᵢ = +15 cm (real). m = −15/10 = −1.5 (inverted, 1.5× larger). Image height = |m| × h₀ = 1.5 × 4 = 6 cm. The MCAT may also ask you to find f from P: if P = +4 D, then f = 1/P = 0.25 m = 25 cm.

Lens Systems and Magnification

When two or more lenses are placed in series (common in microscopes, telescopes, and the human eye model), the image from the first lens becomes the object for the second lens. The total magnification is the product of individual magnifications: M_total = m₁ × m₂ × ... For a two-lens system: (1) use 1/f₁ = 1/d₀₁ + 1/dᵢ₁ to find the first image location; (2) note whether the first image is real (on far side) or virtual (on near side) — this determines d₀₂; (3) the object distance for the second lens is d₀₂ = D − dᵢ₁, where D is the lens separation, with careful attention to signs (if the first image forms beyond the second lens, d₀₂ is negative, meaning a virtual object for lens 2). The compound microscope: a short-focal-length objective lens (f_obj ~ few mm) produces a real, magnified intermediate image just inside the focal point of the eyepiece (f_eye ~ few cm). The eyepiece acts as a magnifying glass, producing a virtual, greatly enlarged final image at the near point of the eye (~25 cm). Angular magnification of a simple magnifier: M = 25 cm / f (for a relaxed eye viewing at infinity) or M = 1 + 25 cm / f (for image at near point). The Keplerian (astronomical) refracting telescope uses two converging lenses: a long-focal-length objective and a short-focal-length eyepiece separated by f_obj + f_eye. Angular magnification M = −f_obj / f_eye, where the negative sign indicates an inverted image (corrected with an erecting prism in terrestrial telescopes). The Galilean telescope uses a converging objective and a diverging eyepiece, producing an upright image. The MCAT may present a passage describing an optical instrument and ask you to calculate total magnification, identify whether the final image is real or virtual, or explain why lenses are spaced as they are. Key principle: the eyepiece always produces a virtual image — the eye cannot focus on a real image placed inside its near point.

Diffraction and Interference

Diffraction is the bending of waves around obstacles and the spreading of waves through openings — it is a wave property, and its observability depends on the ratio of wavelength to aperture size (significant when λ is comparable to or larger than the opening). Interference is the superposition of waves: constructive interference occurs when waves are in phase (path difference = mλ, where m = 0, 1, 2, ...), producing bright fringes; destructive interference occurs when waves are out of phase (path difference = (m + ½)λ), producing dark fringes. Young's double-slit experiment demonstrates light's wave nature: coherent light passing through two slits separated by distance d produces an interference pattern on a screen at distance L. Bright fringes (constructive) satisfy d sin θ = mλ, where m = 0, 1, 2, ... Dark fringes (destructive) satisfy d sin θ = (m + ½)λ. For small angles, sin θ ≈ tan θ ≈ y/L, so the fringe position y_m = mλL/d and fringe spacing Δy = λL/d. Single-slit diffraction: dark fringes occur at a sin θ = mλ (m = 1, 2, 3, ...), where a is the slit width. The central bright fringe is twice as wide as the others. When both single-slit diffraction and double-slit interference occur simultaneously (real double-slit with finite slit width), the interference pattern is modulated by the diffraction envelope — missing orders occur where an interference maximum coincides with a diffraction minimum. Thin-film interference arises from reflections off the top and bottom surfaces of a thin film (soap bubble, oil slick, anti-reflective coating). Key rules: (1) a π (180°) phase shift occurs when light reflects from a medium of higher n; no phase shift when reflecting from a lower n; (2) the path difference within the film is 2nt (where t is thickness, n is film index), because the wave traverses the film twice; (3) constructive interference for reflected light occurs when 2nt = (m + ½)λ (if one reflection has a phase shift) or 2nt = mλ (if zero or two reflections have phase shifts). Anti-reflective coatings use destructive interference at a target wavelength: 2nt = λ/2 for minimum reflection. The MCAT demands qualitative reasoning: given the indices of three layers, determine whether the reflected wave undergoes a net phase shift and whether the film appears bright or dark in reflected light.

Polarization

Polarization describes the orientation of the electric field oscillations in an EM wave. Unpolarized light (e.g., sunlight, incandescent bulbs) has electric field vectors in all directions perpendicular to propagation. A polarizing filter transmits only the component of the electric field parallel to its transmission axis, absorbing the perpendicular component. Malus's law gives the transmitted intensity: I = I₀ cos²θ, where I₀ is the incident intensity after the first polarizer (or the intensity of initially polarized light) and θ is the angle between the light's polarization direction and the filter's transmission axis. For initially unpolarized light passing through a single ideal polarizer, the transmitted intensity is I = I₀/2 (the average of cos²θ over all angles). For two polarizers in series (polarizer-analyzer): if unpolarized light of intensity I₀ hits polarizer 1, I₁ = I₀/2. Then polarizer 2 at angle θ reduces this further: I₂ = I₁ cos²θ = (I₀/2) cos²θ. If the two polarizers are crossed (θ = 90°), I₂ = 0 — no light passes. Three key MCAT facts: (1) Polarization by reflection — light reflected from a non-metallic surface at Brewster's angle θ_B becomes completely polarized parallel to the surface. Brewster's angle satisfies tan θ_B = n₂/n₁. At Brewster's angle, the reflected and refracted rays are perpendicular (θ_B + θ_r = 90°). (2) Polarization by scattering — Rayleigh scattering of sunlight by atmospheric molecules partially polarizes sky light; this is why polarized sunglasses reduce glare from the sky. (3) Polarization by selective absorption (dichroism) — certain materials (Polaroid film) absorb one polarization component. Circular polarization (not heavily tested but worth knowing): results from two perpendicular linearly polarized waves with a 90° phase difference. Optical activity: certain materials (chiral molecules, sugar solutions) rotate the plane of polarization — the rotation angle is proportional to concentration and path length, used in saccharimetry. The MCAT may present a passage on optical rotation as a bridge to organic chemistry (chirality) or biochemistry (glucose measurement).

The Human Eye as an Optical System

The human eye is a compound optical system that produces a real, inverted, diminished image on the retina. Light enters through the cornea (n ≈ 1.38, provides ~70% of the eye's refractive power due to the large index change from air), passes through the aqueous humor, the pupil (aperture control via the iris), the crystalline lens (n ≈ 1.40, provides fine focusing via accommodation), and the vitreous humor, finally forming an image on the retina. The retina's photoreceptors (rods and cones) transduce the inverted image into neural signals — the brain flips the image perceptually. The eye's total optical power is about 60 diopters in the relaxed state (viewing distant objects). Accommodation is the process of increasing lens power to focus on near objects: the ciliary muscles contract, reducing tension on the suspensory ligaments (zonules), allowing the lens to become more spherical (increased curvature, shorter focal length, higher power). The near point is the closest distance at which the eye can focus (typically ~25 cm in young adults, receding with age/presbyopia); the far point is the farthest distance (infinity for a normal/emmetropic eye). Myopia (nearsightedness): the eye is too long or the cornea/lens too powerful, so the image of a distant object focuses in front of the retina. Corrected with a diverging (negative) lens, which spreads rays slightly before they enter the eye. The far point for a myope is finite — the diverging lens takes an object at infinity and produces a virtual image at the eye's far point. Lens power for correction: P = 1/f = −1/(far point distance in meters). Hyperopia (farsightedness): the eye is too short or too weak, so the image of a near object focuses behind the retina. Corrected with a converging (positive) lens. The lens takes an object at the normal near point (25 cm) and produces a virtual image at the hyperope's actual (more distant) near point. Presbyopia: age-related loss of accommodation due to lens stiffening — treated with bifocals or progressive lenses that provide multiple powers. Astigmatism: asymmetric corneal curvature causing different focal lengths in different planes — corrected with cylindrical lenses. The MCAT frequently asks: 'A myopic person has a far point of 50 cm. What power lens corrects their distance vision?' Answer: P = −1/0.50 m = −2.0 D (diverging). The corrected person can now see distant objects clearly. For near vision correction in a hyperope with near point 100 cm: the lens must take an object at 25 cm and produce a virtual image at 100 cm. Using the thin lens equation with d₀ = 25 cm = 0.25 m, dᵢ = −100 cm = −1.0 m (virtual), 1/f = 1/0.25 + 1/(−1.0) = 4 − 1 = 3 ⇒ f = 1/3 m, P = +3.0 D.

How it works

Every optics MCAT problem reduces to four patterns. (1) Ray optics: determine whether the optical element is converging or diverging. Use 1/f = 1/d₀ + 1/dᵢ with the correct sign convention to find image location. Calculate m = −dᵢ/d₀ for size and orientation. Cross-check: a negative m means inverted image; a negative dᵢ means virtual image. (2) Snell's law: identify n₁ and n₂. Rearrange to find the unknown. For critical angle problems, check that n₁ > n₂ (required for TIR), then compute θ_c = sin⁻¹(n₂/n₁). If the given angle exceeds θ_c, light undergoes TIR. (3) Interference: identify the geometry (double-slit, single-slit, or thin film). For slits, write path-difference condition — d sin θ = mλ (bright for double-slit) or a sin θ = mλ (dark for single-slit). For small angles, approximate y ≈ Lθ. For thin films, draw the layer stack, count phase shifts at each reflection (π shift when reflecting from higher n), then apply 2nt = mλ or (m+½)λ depending on net phase shift. (4) Eye/vision: classify the condition (myopia = too strong, hyperopia = too weak). For corrective lens problems, treat the lens + eye as a system. The lens produces a virtual image at the eye's far or near point, which the eye then focuses. Use the thin lens equation to find the required focal length, then P = 1/f. Always check the sign: diverging lenses have negative power. For compound instruments (microscope, telescope), work lens-by-lens: the image from lens 1 becomes the object for lens 2. Total magnification is the product m₁ × m₂. The final image from a microscope or astronomical telescope is inverted; from a Galilean telescope it's upright. The most critical MCAT skill: rapid sign-convention fluency. Practice converting between 'real/virtual/upright/inverted/magnified/diminished' and 'positive dᵢ / negative dᵢ / positive m / negative m' until it is automatic.

How it works

Every optics MCAT problem reduces to four patterns. (1) Ray optics: determine whether the optical element is converging or diverging. Use 1/f = 1/d₀ + 1/dᵢ with the correct sign convention to find image location. Calculate m = −dᵢ/d₀ for size and orientation. Cross-check: a negative m means inverted image; a negative dᵢ means virtual image. (2) Snell's law: identify n₁ and n₂. Rearrange to find the unknown. For critical angle problems, check that n₁ > n₂ (required for TIR), then compute θ_c = sin⁻¹(n₂/n₁). If the given angle exceeds θ_c, light undergoes TIR. (3) Interference: identify the geometry (double-slit, single-slit, or thin film). For slits, write path-difference condition — d sin θ = mλ (bright for double-slit) or a sin θ = mλ (dark for single-slit). For small angles, approximate y ≈ Lθ. For thin films, draw the layer stack, count phase shifts at each reflection (π shift when reflecting from higher n), then apply 2nt = mλ or (m+½)λ depending on net phase shift. (4) Eye/vision: classify the condition (myopia = too strong, hyperopia = too weak). For corrective lens problems, treat the lens + eye as a system. The lens produces a virtual image at the eye's far or near point, which the eye then focuses. Use the thin lens equation to find the required focal length, then P = 1/f. Always check the sign: diverging lenses have negative power. For compound instruments (microscope, telescope), work lens-by-lens: the image from lens 1 becomes the object for lens 2. Total magnification is the product m₁ × m₂. The final image from a microscope or astronomical telescope is inverted; from a Galilean telescope it's upright. The most critical MCAT skill: rapid sign-convention fluency. Practice converting between 'real/virtual/upright/inverted/magnified/diminished' and 'positive dᵢ / negative dᵢ / positive m / negative m' until it is automatic.

Comparisons

• C/P (Waves): Diffraction and interference connect optics to the general wave equation v = fλ. The same mathematics of superposition, path-length difference, and phase applies to sound waves, water waves, and light waves. The MCAT may ask you to compare a double-slit experiment with sound interference from two speakers.
• C/P (Atomic/Nuclear Physics): The photoelectric effect (K_max = hf − φ) connects the EM spectrum section to quantum physics. Light's particle-like behavior (photons) is revealed when high-frequency light ejects electrons from metal surfaces — a direct bridge between optics and modern physics.
• C/P (Electricity and Magnetism): EM waves are oscillating electric and magnetic fields. The speed of light c = 1/√(ε₀μ₀) emerges from Maxwell's equations. Polarization demonstrates the transverse nature of EM waves — the electric field direction defines the polarization axis.
• B/B (Vision): The retina's rod and cone photoreceptors transduce photons into neural signals via the visual phototransduction cascade (rhodopsin → transducin → PDE → cGMP decrease → Na+ channel closure → hyperpolarization). The MCAT integrates physics (optics of the eye) with biology (phototransduction) in passage-based questions.
• B/B (Eye anatomy): Cornea, aqueous humor, lens, vitreous humor, and retina form the optical pathway. The fovea (highest cone density) corresponds to the central visual axis. The optic disk (blind spot) has no photoreceptors — the MCAT may ask why we don't perceive a hole in our visual field (the brain fills it in).
• B/B (Nervous system): Visual information travels from retina → optic nerve → optic chiasm (partial decussation) → LGN of thalamus → primary visual cortex (V1, occipital lobe). The right visual field from both eyes projects to the left hemisphere and vice versa. This is frequently tested in passage-based B/B questions.
• C/P (Biochemistry): Circular dichroism spectroscopy measures the differential absorption of left- and right-circularly polarized light by chiral molecules, used to determine protein secondary structure. Optical rotation is proportional to the concentration of chiral molecules — a link between optics and stereochemistry.

Common confusions

• Getting the sign of dᵢ wrong: For a single converging lens with d₀ > f, dᵢ is positive (real image on far side). But if the first image in a two-lens system falls beyond the second lens, d₀₂ becomes negative (virtual object). Most students miss this — it's tested because it distinguishes memorization from understanding.
• Confusing bright and dark fringe conditions: Double-slit bright fringes: d sin θ = mλ. Single-slit dark fringes: a sin θ = mλ. These use the same equation for opposite fringe types. The MCAT exploits this by asking 'if the slit separation d is halved, what happens to the fringe spacing?' When d decreases, Δy = λL/d increases — fringes spread out.
• Forgetting the phase shift in thin-film interference: Light reflecting from a higher-index medium gains a π (180°) phase shift — equivalent to adding λ/2 to the path. Students often forget to check BOTH interfaces for phase shifts before writing the 2nt condition. The net phase shift determines whether constructive interference requires 2nt = mλ or 2nt = (m+½)λ.
• Using the wrong sign for corrective lens power: Myopia = diverging lens = negative power. Hyperopia = converging lens = positive power. A MCAT distractor often gives the correct magnitude but wrong sign. Always ask: does this condition require light to be spread out (diverging/negative) or focused more (converging/positive)?
• Assuming the eye's lens alone does all the focusing: The cornea provides ~70% of the eye's total refractive power (~42 D of the ~60 D total). The lens contributes only ~18 D in the relaxed state, increasing with accommodation. MCAT passages may test this distribution — a question about corneal transplant or LASIK implicitly references the cornea's dominant role.
• Misapplying Malus's law to unpolarized light: For initially unpolarized light, the first polarizer reduces intensity to I₀/2. Malus's law I = I₀ cos²θ only applies to light that is ALREADY polarized. A two-polarizer problem with unpolarized source gives I_final = (I₀/2) cos²θ, not I₀ cos²θ.

Quick review

• c = fλ = 3.00 × 10⁸ m/s in vacuum. Photon energy E = hf = hc/λ. Higher frequency = higher energy. Spectrum order (low to high f): radio, microwave, IR, visible, UV, X-ray, gamma.
• Law of reflection: θᵢ = θ_r, both measured from the normal. Index of refraction: n = c/v. Light bends toward the normal when entering higher n; away from the normal when entering lower n.
• Snell's law: n₁ sin θ₁ = n₂ sin θ₂. Critical angle: θ_c = sin⁻¹(n₂/n₁). TIR when n₁ > n₂ and θᵢ > θ_c. All incident light reflects — zero transmission.
• Mirror and thin lens equation: 1/f = 1/d₀ + 1/dᵢ. Magnification: m = −dᵢ/d₀. Converging (concave mirror, convex lens): f positive. Diverging (convex mirror, concave lens): f negative.
• Converging lens image: d₀ > 2f → real, inverted, diminished. f < d₀ < 2f → real, inverted, magnified. d₀ < f → virtual, upright, magnified. Diverging lens: ALWAYS virtual, upright, diminished.
• Lens power: P = 1/f (f in meters, P in diopters). Converging = positive D; diverging = negative D. Two-lens system: M_total = m₁ × m₂. Image from lens 1 is object for lens 2.
• Double-slit bright fringes: d sin θ = mλ. Fringe spacing: Δy = λL/d. Single-slit dark fringes: a sin θ = mλ. Thin-film 2nt condition depends on phase shifts at interfaces (π shift when reflecting from higher n).
• Polarization: Malus's law I = I₀ cos²θ for polarized light. Unpolarized light through one polarizer → I = I₀/2. Brewster's angle: tan θ_B = n₂/n₁; reflected light is fully polarized parallel to surface.
• Eye: cornea (~42 D) + lens (~18 D relaxed) = ~60 D total power. Accommodation: ciliary muscle contraction → lens rounds up → shorter f → higher power → focus on near objects.
• Myopia (nearsighted): image focuses in front of retina → corrected with diverging (negative) lens, P = −1/(far point in meters). Hyperopia (farsighted): image focuses behind retina → corrected with converging (positive) lens.