PhysicsICSE Class 10 · Total Internal Reflection

Conditions for Total Internal Reflection, with Applications and Numericals (ICSE Class 10)

Updated 15 October 2026 · Fact-checked

Total internal reflection needs two conditions together: (1) light must travel from an optically denser medium towards a rarer medium, and (2) its angle of incidence in the denser medium must be greater than the critical angle for that pair of media. If either fails, part of the light is refracted out.

TIR needs light going denser to rarer and i larger than C; at smaller angles part of the light always refracts out.

Illustration drawn for QuestionBuddy.

Understand Conditions for Total Internal Reflection

Total internal reflection (TIR) is the complete reflection of light back into a denser medium at its boundary with a rarer medium. It is called *total* because no light is refracted out and practically all of it is reflected; it is *internal* because it happens inside the denser medium.

The two essential conditions.
1. Light must travel from an optically denser medium to an optically rarer medium (for example glass → air, water → air, glass → water).
2. The angle of incidence in the denser medium must be greater than the critical angle $C$ for that pair of media.

Both must hold together.

Why condition 1? Going from rarer to denser (air → glass, water → glass), the ray bends towards the normal, so $r < i$ and $r$ can never reach $90°$ . A refracted ray always exists, however large $i$ is, so TIR is impossible.

Why condition 2? For $i < C$ a refracted ray exists (with weak partial reflection); at $i = C$ it just grazes the surface; only for $i > C$ is there no refracted ray at all.

How to test a situation.
1. Which way is the light going: denser → rarer? If not, stop: no TIR.
2. Find $C$ : $sin C = \frac{1}{μ}$ (to air) or $sin C = \frac{μ _{rarer}}{μ _{denser}}$ .
3. Measure $i$ from the normal and compare with $C$ .

TIR compared with ordinary reflection (qualitative).

Ordinary reflection (plane mirror)	Total internal reflection
Happens at any angle of incidence	Only when $i > C$
Needs a polished or silvered surface	Needs only a boundary with a rarer medium
Some light is absorbed; image less bright	Practically all light is reflected; image brighter
Silvering can tarnish	No coating to tarnish

Applications.

Sparkle of a diamond: its critical angle is only about $24.4°$ , so light entering a well-cut diamond is totally reflected many times before escaping in particular directions.
Optical fibres: a thin glass core is surrounded by a cladding of slightly lower μ. Light entering one end strikes the core walls at angles greater than $C$ and travels along by repeated TIR, even round gentle bends. Used for telephone and internet signals and in endoscopes to see inside the body.
Mirage: on a hot day, air near the road is hotter and optically rarer than the air above. Light from the sky going down at a slant passes into ever rarer layers, bending away from the normal, until at a grazing angle it is totally reflected upward. The eye sees an inverted image of the sky that looks like a pool of water.
Total reflecting prisms in periscopes and binoculars (see the next topic).
Water surface seen from below: viewed at a slant from under water, the surface looks silvery, like a mirror, because of TIR.

Conditions for Total Internal Reflection: formulas and key facts

Critical angle to air: $sin C = \frac{1}{μ}$; μ of the denser medium.
Critical angle between two media: $sin C = \frac{μ _{rarer}}{μ _{denser}}$; Exists only for denser → rarer.
Condition for TIR: $denser \to rarer and i > C$; Both conditions together.

How to solve Conditions for Total Internal Reflection questions

Test the two conditions in order; the first one settles many questions without any calculation.

1Identify the two media and the direction of travel. If rarer → denser, answer 'No TIR' with that reason.
2If denser → rarer, find C: $sin C = \frac{1}{μ}$ or $\frac{μ _{rarer}}{μ _{denser}}$ .
3Find the angle of incidence at the boundary, measured from the normal (use geometry inside prisms or blocks).
4Compare: $i > C$ , TIR; $i = C$ , grazing; $i < C$ , refraction.
5Answer exactly what is asked: Yes/No with a reason, the name of the ray, or a diagram.

Conditions for Total Internal Reflection in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

A mirror-like water surface

Suppose you are snorkelling and look up at the water surface at a slant, so that your line of sight meets it at $60°$ to the normal. (Critical angle of water $\approx 48.6°$ )

What do you see there, and why?

Try it first, then show the solutionSolution

Light reaching your eye from that part of the surface is travelling in water (denser) towards air (rarer).
Its angle of incidence, $60°$ , is greater than $48.6°$ , so it has been totally reflected from the surface.

Answer: A silvery, mirror-like surface reflecting the pool floor: TIR.

Memory hook: From below, water at a slant is a perfect mirror.

Seeing inside the stomach

Imagine a doctor passes an endoscope, a flexible bundle of thin optical fibres, down a patient's throat.

How does light travel round the bends of the fibres, and which two conditions make this possible?

Try it first, then show the solutionSolution

Light inside the glass core (denser) meets the cladding (rarer): condition 1.
The fibres are thin and the bends gentle, so the light meets the walls at angles greater than the critical angle: condition 2, so it is totally reflected again and again.

Answer: By repeated TIR at the core walls, with denser → rarer and $i > C$ at each reflection.

Memory hook: A fibre is a light pipe walled by TIR.

Tricks to remember Conditions for Total Internal Reflection

Short memory aids. Say each one aloud once, then use it on a question the same day.

D-to-R and Bigger than C
'Dense to Rare, Bigger than Critical': DR. BC.
Use it when: Stating the two conditions.
Direction first
Before any calculation ask 'Is it leaving the denser medium?' If not, the answer is No.
Use it when: Questions like water → glass.
Total means nothing escapes
TIR: no refracted ray, all light reflected; a mirror always loses some.
Use it when: Comparing TIR with a plane mirror.
Mirage = hot ground mirror
Hot air near the ground is rarer; grazing light from the sky is turned up like a mirror would.
Use it when: Explaining a mirage.

Conditions for Total Internal Reflection: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Water into glass at a large angle · 1 mark · MCQBoard level

A ray travelling in water strikes a water–glass boundary at an angle of incidence of $70°$ . It will:
(a) be totally reflected
(b) be refracted into the glass, bending towards the normal
(c) be refracted into the glass, bending away from the normal
(d) pass straight through without bending

Try it first, then show the solutionSolution

Water to glass is rarer to denser, so TIR is impossible at any angle; the ray bends towards the normal.

Answer: (b) be refracted into the glass, bending towards the normal

Example 2: Stating and explaining the conditions · 3 marks · Short answerBoard level

(a) State the two conditions necessary for total internal reflection. (b) Explain why total internal reflection cannot occur when light passes from air into glass.

Try it first, then show the solutionSolution

(a) (i) Light must travel from a denser to a rarer medium. (ii) The angle of incidence must be greater than the critical angle. (2)
(b) From air into glass the ray bends towards the normal, so $r < i$ ; $r$ never reaches $90°$ , a refracted ray always exists, and there is no critical angle. (1)

Answer: (a) Denser to rarer; i > C (b) r < i always, so a refracted ray always exists.

Example 3: Why a diamond dulls under water · 3 marks · Short answerHarder board level

A diamond (μ = 2.42) is placed (i) in air, (ii) in water (μ = 1.33). (a) Find its critical angle in each case. (b) A ray inside the diamond meets a face at $30°$ . What happens in each case? (c) Why does a diamond sparkle less under water?

Try it first, then show the solutionSolution

(a) Air: $sin C = \frac{1}{2.42}$ , $C \approx 24.4°$ . Water: $sin C = \frac{1.33}{2.42} \approx 0.55$ , $C \approx 33.3°$ . (1)
(b) In air, $30° > 24.4°$ : TIR. In water, $30° < 33.3°$ : the ray refracts out into the water. (1)
(c) In water the critical angle is larger, so fewer rays are totally reflected inside and more light leaks out. (1)

Answer: (a) About $24.4°$ in air, $33.3°$ in water (b) TIR in air; refraction in water (c) Larger C in water, so fewer total reflections.

Example 4: Light in an optical fibre · 3 marks · Short answerHarder board level

An optical fibre has a core of refractive index 1.48 and a cladding of refractive index 1.46. (a) Work out C where core meets cladding. (b) A ray meets the boundary at $85°$ ; another at $75°$ . What happens to each? (c) Why must the cladding have a lower refractive index than the core?

Try it first, then show the solutionSolution

(a) $sin C = \frac{1.46}{1.48} \approx 0.986$ , so $C \approx 80.6°$ . (1)
(b) $85° > 80.6°$ : TIR, it stays in the core. $75° < 80.6°$ : it refracts into the cladding and is lost. (1)
(c) TIR needs light going from denser (core) to rarer (cladding); a cladding of higher μ would make TIR impossible. (1)

Answer: (a) About $80.6°$ (b) $85°$ : TIR; $75°$ : leaks (c) TIR needs denser → rarer.

Example 5: Into a glass slab from a liquid · 4 marks · Long answerHOTS / competency

A glass slab (μ = 1.6) with parallel faces is immersed in a liquid (μ = 1.2). A ray in the liquid strikes the top face at $60°$ . (a) Find the angle of refraction in the glass. (b) Find the critical angle for the glass–liquid boundary. (c) Is the ray totally reflected at the bottom face? (d) At what angle does it leave the slab?

Try it first, then show the solutionSolution

(a) $sin r = \frac{1.2 s i n 60°}{1.6} \approx 0.65$ , so $r \approx 40.5°$ . (1)
(b) $sin C = \frac{1.2}{1.6} = 0.75$ , so $C \approx 48.6°$ . (1)
(c) The faces are parallel, so the ray meets the bottom face at $40.5° < 48.6°$ : no TIR. (1)
(d) By reversibility it leaves at $60°$ , parallel to its original direction. (1)

Answer: (a) About $40.5°$ (b) About $48.6°$ (c) No (d) $60°$

Example 6: Case study: a mirage on the highway · 4 marks · Case-basedHOTS / competency

On a hot afternoon, a driver notices a shimmering 'puddle' on the tarmac far ahead, which disappears as the car gets nearer.
(a) Which air is optically denser: the air just above the road or the air higher up? Why?
(b) Explain how light from the sky reaches the driver's eye from the road surface.
(c) Which two conditions for TIR are satisfied near the road?
(d) Why is the 'pool' seen only far ahead, never close to the car?

Try it first, then show the solutionSolution

(a) The cooler air higher up is denser; air next to the hot road is hotter and rarer. (1)
(b) Light from the sky travelling down at a slant passes into ever rarer layers, bending away from the normal, until it is totally reflected upward into the driver's eye, which sees an image of the sky on the road. (1)
(c) It travels from denser to rarer air, and at the lowest layer its angle of incidence exceeds the critical angle. (1)
(d) Only light meeting the layers at a grazing angle (very large i) can exceed C; this light reaches the eye from far ahead. Close to the car you look down too steeply. (1)

Answer: (a) The upper, cooler air (b) Gradual bending then TIR upward (c) Denser → rarer; i > C (d) Only grazing rays undergo TIR.

Where students lose marks in Conditions for Total Internal Reflection

The slips examiners see most often, and what to write instead.

Mistake: Ignoring the direction of travel
A ray going from a rarer to a denser medium can never be totally reflected, whatever the angle.
Wrong working
'Water to glass at $70°$ , critical angle $63°$ : $70° > 63°$ , so TIR occurs.'
Right working
'No: water to glass is rarer to denser, so TIR cannot occur.'
Do this: Check condition 1 before comparing angles.
Usually costs: Reported by CISCE examiners for 2025 Q3(i).
Mistake: Drawing when asked to name
Questions that say 'which ray' want the label; a diagram earns nothing unless asked.
Wrong working
Drawing the path of every ray instead of naming one.
Right working
'Ray J', then the diagram only in the part that asks for it.
Do this: Underline the command word: name, state, draw.
Usually costs: Reported for 2025 Q4(i).
Mistake: Stating only one condition
Both conditions are needed; each carries a mark.
Wrong working
'The angle of incidence must be greater than the critical angle.'
Right working
Add: 'and light must go from a denser to a rarer medium.'
Do this: Learn the pair together.
Usually costs: One of the two marks.
Mistake: Saying 'i equal to C' gives TIR
At $i = C$ the ray grazes the surface; TIR needs $i > C$ .
Wrong working
'TIR occurs when the angle of incidence equals the critical angle.'
Right working
'TIR occurs when the angle of incidence is greater than the critical angle.'
Do this: Write 'greater than', never 'equal to'.
Usually costs: The definition mark.

Exam tips

In 2025 Q3(i) the expected answer was 'No', with the reason that TIR cannot occur from a rarer (water) to a denser (glass) medium; the angles were a distraction.
For 'explain using TIR' questions, name the denser and rarer media and say why $i > C$ .
Mirage answers should mention hot (rarer) air near the ground, gradual bending away from the normal, and TIR at grazing incidence.
Mention the cladding of lower refractive index in any optical fibre answer.

Practice questions on Conditions for Total Internal Reflection

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
Total internal reflection is impossible when light travels from:
(a) glass into air
(b) water into air
(c) air into water
(d) diamond into glass
Hint
Which one goes from rarer to denser?
Answer
(c) air into water
Q2 · 2 marks · Short answerBoard level
Name two everyday effects caused by total internal reflection, and for each, name the denser and the rarer medium.
Hint
Think of jewellery and roads on hot days.
Answer
Any two, e.g. sparkle of a diamond (diamond, air); mirage (cooler air above, hot air near the ground); optical fibres (core, cladding); silvery look of a water surface from below (water, air).
Q3 · 2 marks · Short answerHarder board level
The critical angle of water is about $48.6°$ . A ray in water meets the water–air surface at $52°$ . What happens to it? Give a reason.
Hint
Check both conditions.
Answer
It is totally reflected back into the water: it travels from denser to rarer, and $52° > 48.6°$ .
Q4 · 3 marks · Short answerHarder board level
A glass has μ = 1.50 for red light and μ = 1.54 for violet light. A ray of white light inside the glass meets a glass–air surface at $41°$ . Show by calculation which of the two colours stays inside the glass and which gets out.
Hint
Find C for each colour.
Answer
Red: $sin C = \frac{1}{1.50}$ , $C \approx 41.8°$ ; $41° < 41.8°$ , so red escapes. Violet: $sin C = \frac{1}{1.54}$ , $C \approx 40.5°$ ; $41° > 40.5°$ , so violet is totally reflected.
Q5 · 1 mark · Assertion-reasonHarder board level
Assertion (A): A ray going from water into glass at $80°$ is not totally reflected.
Reason (R): Total internal reflection needs light to travel from a denser to a rarer medium.
(a) Both A and R are true and R explains A.
(b) Both are true but R does not explain A.
(c) A is true, R is false.
(d) A is false, R is true.
Hint
Is glass denser or rarer than water?
Answer
(a) Both A and R are true and R explains A.
Q6 · 2 marks · Short answerHarder board level
Give two advantages of total internal reflection over reflection from a silvered plane mirror, and explain the reason for each.
Hint
Brightness and the reflecting surface.
Answer
(1) Brighter image: TIR reflects practically all the light, while a mirror absorbs some. (2) Long-lasting: TIR needs no silvering, so nothing tarnishes or peels. (Also: no multiple images, as from a thick mirror.)
Q7 · 4 marks · Long answerHOTS / competency
A straight acrylic rod (μ = 1.5) is used as a 'light pipe'. A ray enters its flat end face from air at an angle of incidence of $60°$ . (a) Find the angle of refraction at the end face. (b) Find the angle at which this ray meets the side wall of the rod. (c) Is it totally reflected there? (d) Show that even a ray entering at nearly $90°$ is trapped.
Hint
The side wall is perpendicular to the end face, so the angle at the wall is $90° - r$ .
Answer
(a) $sin r = \frac{s i n 60°}{1.5} \approx 0.577$ , $r \approx 35.3°$ . (b) $90° - 35.3° = 54.7°$ . (c) Yes: C for acrylic is about $41.8°$ and $54.7° > 41.8°$ . (d) The largest possible $r$ is $41.8°$ (for $i \to 90°$ ), so the wall angle is at least $90° - 41.8° = 48.2° > 41.8°$ : always TIR.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.The two conditions for TIR?Show answer
Denser to rarer, and angle of incidence greater than the critical angle.
2.Can TIR occur when light goes from water into glass?Show answer
No.
3.Why does a diamond sparkle?Show answer
Its small critical angle (about $24.4°$ ) causes repeated TIR inside it.
4.In an optical fibre, is the core or the cladding denser?Show answer
The core.
5.Which layer of air is rarer in a mirage on a road?Show answer
The hot air next to the road.

Conditions for Total Internal Reflection: frequently asked questions

What are the conditions for total internal reflection?

Light must be travelling from an optically denser medium to a rarer one, and its angle of incidence in the denser medium must be greater than the critical angle for that pair of media.

Why can't total internal reflection happen from air to glass?

Going into glass, light bends towards the normal, so the angle of refraction is always smaller than the angle of incidence and never reaches 90°. A refracted ray always exists, so there is no total reflection.

How is total internal reflection different from reflection by a mirror?

TIR happens only for angles above the critical angle at a boundary with a rarer medium, and reflects practically all the light. A mirror reflects at any angle but absorbs some light, and its silvering can tarnish.