NDA Physics · Light and Optics

Refraction, Speed of Light, and Total Internal Reflection

Light bends when it changes medium because its speed changes — toward the normal entering a denser medium, away from it entering a rarer one. Refractive index n = c/v measures the slow-down. Past a critical angle, light going denser-to-rarer is reflected back entirely (TIR), which powers the mirage and optical fibre.

All Light and Optics notes NDA Physics strategy

Why this matters

Seventeen PYQs and a rich vein of EASY recall plus clean numerics. The recurring tests are: which way light bends, the constant-frequency fact, n = c/v (so higher n means lower speed), speed ratios between media, and the everyday effects — raised pool bottom, twinkling stars, the early sunrise, the mirage, and the optical fibre. The single HARD question here is a TIR retrace-the-path geometry problem.

Concept 1 of 5: Refraction and Snell's law

When light crosses into a new medium its speed changes, and that forces the ray to change direction — unless it hits the surface dead-on. Going into a denser medium (slower) it bends TOWARD the normal; coming out into a rarer medium (faster) it bends AWAY. One thing never changes across the boundary: the frequency.

Definition

Snell's law: $n_1 \sin\theta_1 = n_2 \sin\theta_2$ — relates the angles to the refractive indices on each side.

Rarer → denser: ray bends toward the normal.
Denser → rarer: ray bends away from the normal.
Normal incidence (angle 0°): the ray goes straight through, unbent, even though its speed still changes.

Across the boundary the frequency stays the same (it is set by the source); the speed and wavelength change together, and the colour (which tracks frequency) is preserved.

Snell's law of refraction

n_1 \sin\theta_1 = n_2 \sin\theta_2

n_1, n_2refractive indices of the two media
$\theta_1$ angle of incidence (from the normal)
$\theta_2$ angle of refraction (from the normal)

Worked example

A ray of light passes from air into water at an angle of incidence of 0° (straight down onto the surface). What happens to its direction and frequency?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

NDA · Apr 2021 · Q92Moderate

Example 1 · Light and Optics · Refraction, Speed of Light and TIR

Light waves are incident on an air-glass boundary. Some of the light waves are reflected and some are refracted in the glass. Which one of the following properties is the same for the incident wave and the refracted wave ?

Frequency is the invariant — not speed or wavelength

When asked what stays the same across a refraction boundary, the answer is always frequency. Speed and wavelength both change (in proportion); direction changes unless incidence is 0°.

Normal incidence still slows the light

At 0° incidence the ray does not bend, but it does change speed (and wavelength). 'No bending' is not the same as 'no change'.

Drill 4 more on refraction and snell's law

Concept 2 of 5: Refractive index — n = c/v

Refractive index just measures how much a medium slows light down. The bigger the n, the slower light moves through it (and the more it bends). Since light is fastest in vacuum, n is always greater than 1 for any real material — and a denser medium has the bigger n and the smaller speed.

Definition

The (absolute) refractive index is $n = c/v$ , the ratio of the speed of light in vacuum to its speed in the medium.

$n > 1$ for every material medium (light is slowest in matter, fastest in vacuum).
Higher $n$ ⟹ lower speed $v$ (inverse relationship): $v = c/n$ .
Comparing two media, $\dfrac{v_1}{v_2} = \dfrac{n_2}{n_1}$ — the speed ratio is the INVERSE of the index ratio.

Refractive index and speed

n = \dfrac{c}{v} \quad\Rightarrow\quad v = \dfrac{c}{n}, \qquad \dfrac{v_1}{v_2} = \dfrac{n_2}{n_1}

nrefractive index of the medium
cspeed of light in vacuum (≈ 3 × 10⁸ m/s)
vspeed of light in the medium

Worked example

The refractive index of a glass is 1.5. If the speed of light in vacuum is c, what is the speed of light in this glass?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

NDA · Sep 2022 · Q133Moderate

Example 2 · Light and Optics · Refraction, Speed of Light and TIR

The refractive index of crown glass is close to 3/2. If the speed of light in air is

c

, then the speed of light in the crown glass will be close to

Speed is the INVERSE of refractive index

Higher n means slower light, not faster. When comparing two media, flip the ratio: v₁/v₂ = n₂/n₁. The most-missed step is keeping the index ratio instead of inverting it.

Drill 7 more on refractive index — n = c/v

Concept 3 of 5: Everyday refraction effects

Refraction explains a whole cluster of familiar sights: a pool looks shallower than it is, a coin or lemon in water looks raised and bigger, stars twinkle, and the Sun is visible a little before it actually rises. All of these are the same idea — light bending as it passes through media (or air layers) of different density.

Definition

Refraction at work in everyday life:

Apparent depth: the bottom of a water tank looks raised (apparent depth = real depth / n). A lemon or coin in water looks shallower and larger.
Twinkling of stars: starlight passes through air layers of varying density and refracts continually, so the star's apparent position and brightness flicker. (Planets twinkle far less.)
Early sunrise / late sunset: atmospheric refraction bends sunlight over the horizon, so we see the Sun a couple of minutes before it actually rises and after it sets.

These are refraction effects — distinct from scattering (which colours the sky).

Worked example

A coin lies at the bottom of a 1.6 m deep tank of water (n = 4/3). At what depth does it appear to be when viewed from straight above?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

NDA · Sep 2025 · Q69Easy

Example 3 · Light and Optics · Refraction, Speed of Light and TIR

Bottom of a tank containing water appears to be raised. It is due to

Twinkling = refraction; blue sky / red sunset = scattering

Twinkling of stars and the early sunrise are REFRACTION effects. The blue colour of the sky and the red of sunset are SCATTERING (covered in Light Phenomena). Don't mix the two up — NDA tests both in the same paper.

Drill 2 more on everyday refraction effects

Concept 4 of 5: Total internal reflection and the critical angle

When light tries to leave a denser medium for a rarer one, it bends away from the normal — and as you increase the incidence angle, the refracted ray tilts further until, at the critical angle, it grazes the surface. Push past that angle and the light cannot escape at all: it is reflected entirely back inside. That all-or-nothing reflection is total internal reflection.

Definition

Total internal reflection (TIR) occurs when light travels from a denser to a rarer medium AND the angle of incidence exceeds the critical angle $\theta_c$ .

At the critical angle the refracted ray grazes along the surface (angle of refraction = 90°).
Critical angle: $\sin\theta_c = \dfrac{n_2}{n_1} = \dfrac{1}{n}$ (for a medium of index n against air).
Two conditions are BOTH required: denser → rarer, and incidence > critical angle.

Higher refractive index ⟹ smaller critical angle (light is trapped more easily).

Critical angle

\sin\theta_c = \dfrac{1}{n}

$\theta_c$ critical angle (denser→rarer)
nrefractive index of the denser medium (vs air)

TIR happens only when light goes from a denser to a rarer medium and the angle of incidence exceeds the critical angle. It powers optical fibres and the desert mirage.

Worked example

A medium has refractive index 2. Find its critical angle for light going from the medium into air.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

NDA · Apr 2021 · Q99Moderate

Example 4 · Light and Optics · Refraction, Speed of Light and TIR

Mirage is an illustration of

TIR only goes denser → rarer

Total internal reflection cannot occur when light enters a denser medium. The light must be in the denser medium trying to escape into the rarer one. Miss this and the whole setup is wrong.

Both conditions, not just a big angle

A large angle of incidence alone is not enough — it must EXCEED the critical angle, and the direction must be denser-to-rarer. At exactly the critical angle you get grazing refraction, not TIR.

Drill 2 more on total internal reflection and the critical angle

Concept 5 of 5: Mirage and the optical fibre

Total internal reflection is not just a lab curiosity — it makes the shimmering 'water' on a hot road and carries your internet down a glass thread. On a hot day, layers of air near the ground act like media of decreasing density, so light from the sky bends and finally reflects, fooling you into seeing a pool. An optical fibre traps light by bouncing it off its walls again and again, never letting it leak out.

Definition

Applications of TIR:

Mirage (desert / hot road): hot air near the ground is rarer than the cooler air above; light from the sky refracts through these layers and undergoes total internal reflection, so the ground looks like a reflecting water surface. (It involves BOTH progressive refraction AND total internal reflection.)
Optical fibre: light entering one end strikes the walls beyond the critical angle and is totally internally reflected over and over, travelling a zig-zag path with almost no loss — even around bends.
Also: sparkle of diamonds (small critical angle ≈ 24°), prism periscopes, and endoscopes.

Worked example

Explain why light can travel along a long, curved optical fibre without escaping through its sides.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

NDA · Sep 2019 · Q86Easy

Example 5 · Light and Optics · Refraction, Speed of Light and TIR

Light rays move in straight lines. But through an optical fibre, they can move in any type of zigzag path because

Mirage is TIR, not simple reflection or dispersion

A mirage is often miscalled 'reflection' or 'dispersion'. It is total internal reflection (preceded by gradual refraction through hot-air layers). The desert/hot-road illusion is the standard NDA cue for TIR.

Drill 2 more on mirage and the optical fibre

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

Refraction and Snell's law
Snell's law of refraction
$n_1 \sin\theta_1 = n_2 \sin\theta_2$
Refractive index — n = c/v
Refractive index and speed
$n = \dfrac{c}{v} \quad\Rightarrow\quad v = \dfrac{c}{n}, \qquad \dfrac{v_1}{v_2} = \dfrac{n_2}{n_1}$
Total internal reflection and the critical angle
Critical angle
$\sin\theta_c = \dfrac{1}{n}$

Watch out for (7)

Frequency is the invariant — not speed or wavelength
→ Refraction and Snell's law
Normal incidence still slows the light
→ Refraction and Snell's law
Speed is the INVERSE of refractive index
→ Refractive index — n = c/v
Twinkling = refraction; blue sky / red sunset = scattering
→ Everyday refraction effects
TIR only goes denser → rarer
→ Total internal reflection and the critical angle
Both conditions, not just a big angle
→ Total internal reflection and the critical angle
Mirage is TIR, not simple reflection or dispersion
→ Mirage and the optical fibre

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