Chapter 9 - Ray Optics and Optical Instruments

Imagine throwing a rubber ball at a smooth wall. It bounces back with the same angle it came in. Light does the same. Law of reflection: incident angle equals reflected angle i = r, both measured from normal. Incident ray, reflected ray and normal all lie in one plane. A plane mirror forms virtual image behind it. Think of ball bounce - real images can be caught on a screen like cinema, virtual images can only be seen, like your image in a mirror.

Now picture a fast car running on a road and entering soft sand. It slows down. When one wheel hits sand earlier, the car turns. Light bends the same way when changing medium. This is refraction. Snell's law: n1 sin i = n2 sin r. Refractive index n = c / v, where c is speed in vacuum 3x10^8 m/s, v speed in medium. If light goes rarer to denser, it bends towards normal because it slows. Denser to rarer, away from normal.

Daily life: Pencil in water glass looks bent at surface because light from pencil in water bends away at water-air. Swimming pool looks shallower than real. Apparent depth = real depth / n. Real depth 2 m water n=1.33 looks 1.5 m. This is dangerous - never judge depth by looking.

Look at a steel spoon. Inside of spoon is concave, outside is convex. This is the whole world of spherical mirrors. A spherical mirror is part of a hollow sphere. Centre of sphere is C, pole P is centre of mirror, R = PC, focal length f = R/2.

Inner spoon - concave mirror: Bowl collects light. Parallel rays meet at focus in front. f is negative as per sign convention (if incident from left). It is converging. Use: shaving mirror and makeup mirror - when face between F and P, magnified erect virtual. Torch searchlight - filament at F, beam parallel. Dentist mirror - magnified teeth. Solar cooker - collects sun at focus.

Outer spoon - convex mirror: Hill spreads light. It diverges parallel rays, focus behind mirror. f positive. Wide view, always virtual diminished erect. Use: car side mirrors - wide field, small image, so text Objects closer than they appear. Street turning mirrors, security mirrors in shops.

Mirror formula: 1/f = 1/v + 1/u (with sign). Magnification m = -v/u = height image / height object. Negative means inverted real, positive erect virtual.

Think of funnel vs hill. Convex lens thick in middle like funnel collecting water - collects light, converging. Concave lens thin in middle thick at edges like hill spreading water - diverges light, diverging.

Convex lens can form real image on opposite side like camera. When object outside F, real inverted can be on screen. When object inside F, within focal length, virtual erect magnified like magnifying glass.

Lens maker's formula tells focal length from material and curvature: 1/f = (n-1)(1/R1 - 1/R2). R1 first surface, R2 second. R positive if outward bulging in direction of incident light. n refractive index of glass ~1.5.

Lens formula: 1/f = 1/v - 1/u (sign wise difference from mirror). Magnification m = v/u = hi/ho. Power P = 1/f in meters, unit dioptre D. For contact combination: P = P1+P2, 1/f = 1/f1+1/f2.

Daily uses: Magnifying glass reading small print, watch repair - ant under lens looks huge virtual erect when within F-O. Camera convex forms real inverted small on film. Myopia spectacles use concave diverging.

6 positions for convex lens: infinity image at F tiny, beyond 2F image between F&2F real small, at 2F at 2F same, between 2F&F beyond 2F magnified, at F at infinity huge, within F on same side virtual erect magnified.

When light goes from denser to rarer, it bends away from normal. If incident angle grows, refracted angle reaches 90 degrees. That incident angle is critical angle c. Formula sin c = n2 / n1, where n1 denser, n2 rarer. Beyond c, no refraction, all light reflects back inside - Total Internal Reflection TIR. 100% reflection, brighter than mirror which absorbs some.

Values: water-air n 1.33→1, sin c=1/1.33, c≈48.75°. Glass-air 1.5→1, c≈41.8°. Diamond-air n=2.42, c≈24.4° - very small, so light traps inside diamond many times - sparkle.

Conditions: must go denser to rarer, and i greater than c.

Daily life: Mirage in desert - hot air near ground less dense, rarer. Light from sky coming down enters rarer and rarer layers, i increases, TIR occurs, sky appears as water illusion. Diamond sparkle - multiple TIR due to small critical angle, cut to trap light.

Optical fibre: core refractive index ~1.52, cladding ~1.48, core denser. Light enters and keeps TIR zigzag inside like water slide tunnel. Even if fibre bends, light trapped. Uses: internet high speed data, telephone, endoscopy to see inside body, decorative lamps.

Prism is triangular glass with angle A. Light entering bends towards base. Deviation delta = i + e - A, where i incidence, e emergence. Minimum deviation delta_m occurs when i = e symmetric. Then refractive index n = sin[(A+delta_m)/2] / sin(A/2).

White light is mix of colours. Refractive index depends on wavelength, violet slows more so n_violet greater than n_red. So white splits into VIBGYOR - dispersion. Violet deviates most, red least. Imagine crowd running on road enters sand - slower persons turn more. Violet is slowest, turns most.

Rainbow: water droplets are tiny prisms plus TIR mirrors. Sun behind observer. Sunlight enters droplet, refracts and disperses, reflects internally via TIR at back, refracts again exiting, arc opposite sun. Primary rainbow violet inner red outer. Secondary two TIR, dimmer reversed.

Daily visuals: CD rainbow - grooves act as grating diffracts. Soap bubble colours - interference of thin film, different thickness colours.

Eye is natural camera. Parts: cornea - outer bulge, transparent, most refraction 2/3 power. Iris - coloured diaphragm controls light, like aperture ring. Pupil - opening in iris, changes size. Eye lens - convex flexible held by ciliary muscles, accommodation changes focal length. Retina - film screen, has rods low light black-white, cones colour bright. Optic nerve to brain, brain erects inverted image.

Near point D = 25 cm least distance clear vision, far point infinity.

Defects: Myopia - image before retina, elongated eyeball or excess power, far blurry. Correction concave diverging pushes back. Think projector too close before screen, need diverging to push back. Hypermetropia - image beyond retina, short eyeball less power, near blurry. Correction convex converging pulls forward. Projector too far beyond screen, need converging. Astigmatism - cornea uneven, different curvatures, cylindrical lens. Presbyopia - age 40+, ciliary weak, accommodation less, near far both issues, bifocal.

Eye vs camera side by side: eye lens = camera lens, iris = aperture diaphragm, pupil = aperture opening, retina = film sensor, ciliary = focus ring.

Simple microscope - single convex lens with object within F-O. Virtual erect magnified huge upright. Use: watch repair reading small print, detective seeing tiny. Magnification M = 1 + D/f when image at near point D 25 cm, M = D/f when at infinity relaxed eye.

Compound microscope - two convex lenses: objective small fo near object forms real inverted magnified intermediate image at tube length L, eyepiece fe acts as simple microscope magnifies that. Total M = Mo × Me. Mo = -L / fo (negative inverted), Me = 1 + D/fe near, Me = D/fe infinity. Final virtual inverted greatly magnified. Use: cells bacteria. L = distance between objective image and eyepiece ~ tube length.

Telescope is opposite microscope - far objects huge distance. Big objective is light bucket - large aperture collects faint star light like bucket collecting rain. Forms small real inverted image at focal plane.

Astronomical telescope - two convex: objective fo large big bucket, eyepiece fe small. Final image at infinity M = -fo / fe (negative inverted), tube length L = fo + fe. Near point image at D: M = -fo/fe (1+fe/D), L = fo + fe + fe*D/(D+fe) approx fo+fe. Magnification high needs large fo small fe.

Reflecting telescope - uses concave mirror as objective light bucket, eliminates chromatic aberration because mirror no dispersion, also no spherical if parabolic. Cassegrain has secondary convex mirror. Kids seeing moon stars in observatory.