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

Intuition

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_1angle of incidence (from the normal)
\theta_2angle 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?

At 0° incidence the ray travels along the normal, so $\sin\theta_1 = 0$ forces $\sin\theta_2 = 0$ — no bending.
The ray goes straight through, though it slows down in the water.
Frequency is set by the source and is unchanged across the boundary.

Answer:It goes straight (undeviated); its frequency is unchanged (speed and wavelength decrease).

Practice this conceptself-check · 4 quick reps

Try it yourself

Light passes from air into glass. Which one of these is the SAME for the incident and refracted wave: speed, direction, wavelength, or frequency?

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

1.
Light going from air into water bends toward or away from the normal?
2.
Which quantity is unchanged when light refracts: speed, frequency, or wavelength?
3.
At 0° angle of incidence, does the ray bend?
4.
Denser-to-rarer: bends toward or away from normal?

From the bank · past-year question

Example 1Light and OpticsMODERATE

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 ?

[Q92 · Apr · 2021]

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 3 more on refraction and snell's law

Concept 2 of 5

Refractive index — n = c/v

Intuition

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?

Use $v = c/n$ .
$v = c / 1.5 = 2c/3$ .
So light travels at two-thirds of its vacuum speed in this glass.

Answer:

v = (2/3)c

Practice this conceptself-check · 4 quick reps

Try it yourself

Two media have refractive indices 4/3 (water) and 3/2 (glass). What is the ratio of the speed of light in glass to that in water?

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

1.
If n = 2, the speed of light in the medium is what fraction of c?
2.
Higher refractive index means higher or lower light speed?
3.
Refractive index of any real medium (vs air) is always…
4.
Medium A has n = 1.4, medium B has n = 1.8. Which has faster light?

From the bank · past-year question

Example 2Light and OpticsMODERATE

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

[Q133 · Sep · 2022]

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 5 more on refractive index — n = c/v

Concept 3 of 5

Everyday refraction effects

Intuition

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?

Apparent depth = real depth / n.
$= 1.6 / (4/3) = 1.6 \times 3/4 = 1.2$ m.
So the bottom appears raised — at 1.2 m instead of 1.6 m.

Answer:1.2 m (the bottom looks raised by 0.4 m).

Practice this conceptself-check · 4 quick reps

Try it yourself

Why does the Sun appear to rise a few minutes before it has geometrically risen above the horizon?

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

1.
Why does a tank bottom appear raised?
2.
Twinkling of stars is due to atmospheric…
3.
Apparent depth of an object 2 m deep in water (n = 4/3)?
4.
A lemon in water looks larger because of…

From the bank · past-year question

Example 3Light and OpticsEASY

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

[Q69 · Sep · 2025]

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

Intuition

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_ccritical 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.

Use $\sin\theta_c = 1/n$ .
$\sin\theta_c = 1/2$ , so $\theta_c = 30°$ .
Any ray hitting the surface at more than 30° is totally internally reflected.

Answer:

\theta_c = 30°

Practice this conceptself-check · 4 quick reps

Try it yourself

Light is travelling inside a glass block toward its surface with air outside. State the two conditions needed for total internal reflection to occur.

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

1.
TIR happens going from which medium to which?
2.
Critical angle of a medium with n = √2?
3.
At the critical angle, the angle of refraction is…
4.
Higher refractive index gives a larger or smaller critical angle?

From the bank · past-year question

Example 4Light and OpticsMODERATE

Mirage is an illustration of

[Q99 · Apr · 2021]

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 1 more on total internal reflection and the critical angle

Concept 5 of 5

Mirage and the optical fibre

Intuition

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.

The fibre core is optically denser than its surrounding cladding.
Light entering the core strikes the core-cladding boundary at an angle greater than the critical angle.
So it is totally internally reflected at every bounce, repeating all the way along — even round bends — losing almost no energy.

Answer:Repeated total internal reflection traps the light inside the core.

Practice this conceptself-check · 4 quick reps

Try it yourself

A mirage seen on a hot desert road is an example of which optical phenomena?

Practice — Level 1 (4 reps)

Quick reps to lock in the method. Try each, then check.

1.
An optical fibre carries light by repeated…
2.
A desert mirage is based on which phenomenon?
3.
The brilliance/sparkle of a diamond is due to…
4.
Can an optical fibre guide light around a bend?

From the bank · past-year question

Example 5Light and OpticsEASY

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

[Q86 · Sep · 2019]

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

Mastery check — 5 interleaved questions

Try each one before clicking. Questions are interleaved across the concepts above, not grouped — interleaving sharpens transfer.

Example 1Light and OpticsMODERATE

If a ray of light enters from a rarer medium to a denser medium at zero angle of incidence, it would

[Q98 · Apr · 2021]

Example 2Light and OpticsEASY

Which one of the following statements about the refractive index of a material medium with respect to air is correct?

[Q103 · Apr · 2018]

Example 3Light and OpticsEASY

A lemon kept in water in a glass tumbler appears to be larger than its actual size. It is because of

[Q87 · Apr · 2020]

Example 4Light and OpticsHARD

A glass slab (refractive index 1.5) is cut as parallelogram ABCD with BC polished as a reflector. Light is incident at AB from inside at

\pi/3

. Which angle

ABC = \theta

causes reflected light to retrace its path?

[Q74 · Apr · 2026]

Example 5Light and OpticsMODERATE

Mirage is an illustration of

[Q99 · Apr · 2021]

Drill every past-year question on this subtopic

17 questions from the bank — paginated, with cart and Word-export support.

Drill the 17 questions