Understanding Light
Light travels in straight lines — until it hits something. This guide covers what happens when light bounces off a surface (reflection), bends at a boundary (refraction), gets trapped inside a medium (total internal reflection), and gets focused by mirrors and lenses.
When light hits a surface, it bounces off. The angle it arrives at equals the angle it leaves — both measured from the normal (a line perpendicular to the surface at the point of contact). This is the law of reflection, and it applies to every reflective surface from a mirror to a calm lake.
Angles in optics are always measured from the normal because the normal is perpendicular to the surface at the exact point of reflection — it gives a consistent reference regardless of how the surface is tilted. If you measured from the surface, a ray coming in at 0° would be grazing along it, which is confusing. Measured from the normal, 0° means straight in, 90° means parallel to the surface.
The angle of incidence θᵢ = 55°
b) An object is 60 cm from a plane mirror. Where is the image, and what are its characteristics?
c) Why does a mirror reverse left and right, but not up and down?
a) θᵣ = θᵢ = 50° from the normal.
b) Image is 60 cm behind the mirror. It is virtual, upright, same size, and laterally inverted.
c) A mirror doesn't really reverse left-right — it reverses front-to-back (depth). When you raise your right hand, the image raises its right hand too. The apparent left-right reversal happens because you mentally rotate the image to face you.
When light passes from one medium into another, its speed changes. If it hits the boundary at an angle, one side of the wavefront slows down before the other — causing the ray to bend. This is refraction. The index of refraction n tells you how much a medium slows light down compared to a vacuum.
Imagine a row of soldiers marching in step across a field. When they hit a muddy patch at an angle, the soldiers on one end hit the mud first and slow down. The line pivots — bending toward the mud. Light does exactly this at a boundary: entering a denser medium (higher n, slower speed) bends toward the normal.
The ray bends toward the normal (smaller angle) because water is denser.
Bends away from normal — going into less dense medium.
b) Light travels from glass (n=1.60) to water (n=1.33) at θ₁=30°. Find θ₂.
c) Light enters water from air. Does it bend toward or away from the normal? Why?
a) n = c/v = (3 × 10⁸) / (2.4 × 10⁸) = 1.25
b) 1.60 × sin30° = 1.33 × sinθ₂ → sinθ₂ = (1.60 × 0.5)/1.33 = 0.601 → θ₂ = 36.9° (bends away from normal, going less dense)
c) Toward the normal. Water has higher n than air, so light slows down. The side of the wavefront hitting water first slows, bending the ray toward the normal.
When light tries to leave a dense medium at a steep angle, Snell's Law would require sinθ₂ > 1 — which is impossible. Instead, all the light reflects back inside. This is total internal reflection (TIR), and it only occurs going from a denser medium to a less dense one.
sin θc = n₂ / n₁ (where n₁ > n₂)
Any angle greater than θc → total internal reflection. Any angle less → light partially escapes (with partial reflection).
Any ray hitting the glass-air boundary at more than 41.8° from the normal reflects entirely back into the glass.
Light stays trapped in the fibre core as long as it strikes the core-cladding wall at an angle greater than 69.3° from the normal.
Very small critical angle — almost any ray inside a diamond undergoes TIR. This is why diamonds sparkle: light bounces around inside many times before escaping.
b) Can TIR occur when light goes from air into glass? Why or why not?
c) Why must an optical fibre's cladding have a lower index of refraction than the core?
a) sinθc = 1.00/1.33 = 0.752 → θc = 48.8°
b) No. TIR only occurs going from a denser medium to a less dense one. Air (n≈1.00) is less dense than glass (n≈1.50), so light going air→glass bends toward the normal and always passes through — it never hits the critical angle condition.
c) TIR requires going from high n to low n. If cladding had equal or higher n than the core, light would refract out of the core instead of reflecting, and the fibre would lose signal.
Curved mirrors focus or spread reflected rays. A concave (converging) mirror curves inward and can form real images. A convex (diverging) mirror curves outward and always forms virtual, upright, smaller images. Both obey the same mirror equation.
1/f = 1/dₒ + 1/dᵢ m = −dᵢ/dₒ
Sign conventions: concave f > 0, convex f < 0 · real image dᵢ > 0 (in front of mirror) · virtual image dᵢ < 0 (behind mirror) · m > 0 means upright, m < 0 means inverted.
Positive dᵢ → real image, in front of the mirror.
Negative m → inverted. |m| = 0.5 → image is half the size of the object.
Negative dᵢ → virtual image, behind the mirror.
Positive m → upright. |m| = 0.4 → image is 40% the size of the object. This is the typical car side-mirror result: smaller, upright, wider field of view.
b) Concave mirror f=10 cm, object at 5 cm (inside focal point). Find dᵢ — what type of image?
c) Why does a convex mirror always produce a smaller, upright, virtual image?
a) 1/dᵢ = 1/10 − 1/40 = 4/40 − 1/40 = 3/40 → dᵢ = 13.3 cm (real). m = −13.3/40 = −0.33 (inverted, reduced).
b) 1/dᵢ = 1/10 − 1/5 = 1/10 − 2/10 = −1/10 → dᵢ = −10 cm (virtual, behind mirror). Image is upright and magnified — this is how a shaving/makeup mirror works.
c) For a convex mirror, f is negative. The mirror equation always gives dᵢ between −f and 0 (virtual, behind), and m between 0 and +1 (upright, smaller). The diverging nature of the mirror means reflected rays never converge to form a real image.
Lenses refract light to form images. A converging (convex) lens brings parallel rays to a focal point on the far side; a diverging (concave) lens spreads them out. The thin lens equation is identical in form to the mirror equation — but for lenses, real images form on the opposite side from the object (dᵢ > 0).
Mirror: real image in front (same side as object), dᵢ > 0.
Lens: real image behind (opposite side from object), dᵢ > 0.
Virtual images: behind mirror / same side as object for lens — both give dᵢ < 0.
Positive → real image on the far side of the lens.
Inverted, half-size real image.
Negative → virtual image on the same side as the object.
Upright, reduced. This is how diverging lenses correct nearsightedness — they form a virtual image closer than the actual object, within the eye's focus range.
b) Converging lens, object placed exactly at f. Where does the image form, and why?
c) What is the practical difference between a real image and a virtual image — which one can be projected onto a screen?
a) 1/dᵢ = 1/12 − 1/36 = 3/36 − 1/36 = 2/36 → dᵢ = 18 cm. m = −18/36 = −0.5 (inverted, half-size).
b) When dₒ = f: 1/dᵢ = 1/f − 1/f = 0 → dᵢ = ∞. The refracted rays are parallel — the image forms at infinity. This is how a projector lens works (object just inside f → image at a finite but very large distance).
c) A real image is formed by actual converging rays — it can be projected onto a screen (cinema projector, camera sensor). A virtual image is formed by diverging rays that only appear to come from a point — it cannot be projected, only seen by looking through the lens or mirror (magnifying glass, plane mirror).