Total Internal Reflection ICSE Class 10: Critical Angle and Total Reflecting Prisms

What Total Internal Reflection is about

Weightage: CISCE publishes no chapter or unit weightage for ICSE Physics. Total Internal Reflection is in the 2. Light (ii) part of the 2027 syllabus and can be asked in both Section A and Section B of the 80-mark paper.Source: CISCE ICSE Physics (Science Paper 1) syllabus, examination year 2027

Key concepts

From denser to rarer at increasing angles

A ray goes from glass (denser) into air (rarer):
1. **Small $i$**: it refracts out, bending away from the normal ($r>i$); a weak reflected ray also returns into the glass.
2. **$i=C$** (critical angle): the refracted ray grazes the surface ($r=90^{\circ }$).
3. **$i>C$: no refracted ray; all the light is reflected back into the glass: total internal reflection**.

The critical angle is the angle of incidence in the denser medium for which the angle of refraction in the rarer medium is $90^{\circ }$.

Worked example

The critical angle of a glass is 42°. What happens to rays inside it striking a glass–air surface at (a) 30°, (b) 42°, (c) 60°?

Try it first, then show the solutionSolution

1. (a) $30^{\circ }<C$: refracted into air, bending away from the normal (with partial reflection).
2. (b) $i=C$: refracted ray grazes the surface ($r=90^{\circ }$).
3. (c) $60^{\circ }>C$: totally internally reflected.

Answer: (a) refracts out (b) grazes the surface (c) TIR

Critical angle and refractive index

At the critical angle, applying Snell's law from the denser medium to air with $r=90^{\circ }$ gives
$\mu =\frac{1}{\sin C}$,
where $\mu$ is the refractive index of the denser medium with respect to air.

Typical values: glass ($\mu =1.5$): $C\approx 42^{\circ }$; water ($\mu =\frac{4}{3}$): $C\approx 48.6^{\circ }$; diamond ($\mu =2.42$): $C\approx 24.4^{\circ }$.

A larger $\mu$ means a smaller $C$. Since $\mu$ is larger for violet than for red, the critical angle is smaller for violet than for red. For a boundary between two media, $\sin C=\frac{{\mu }_{\text{rarer}}}{{\mu }_{\text{denser}}}$.

Worked example

Find the critical angle of glass of refractive index 1.5.

Try it first, then show the solutionSolution

1. $\sin C=\frac{1}{1.5}=0.667$.
2. $C\approx 41.8^{\circ }$, i.e. about $42^{\circ }$.

Answer: About 42°

Conditions for total internal reflection

Both must hold:
1. Light must travel from an optically denser medium to a rarer medium.
2. The angle of incidence in the denser medium must be greater than the critical angle for that pair of media.

TIR can never happen when light goes from a rarer medium into a denser one (for example from water into glass), however large the angle.

Worked example

A ray in water meets a glass surface at $70^{\circ }$. The critical angle for the glass–water pair is about $63^{\circ }$. Does TIR occur?

Try it first, then show the solutionSolution

1. Water ($\mu \approx 1.33$) is rarer than glass ($\mu =1.5$).
2. Going from rarer to denser, TIR is impossible; the ray refracts into the glass, bending towards the normal.
3. Even though $70^{\circ }$ is larger than $63^{\circ }$, the first condition (denser to rarer) fails, so the comparison with $C$ does not matter.

Answer: No: the light goes from rarer to denser.

Right-angled (45°, 45°, 90°) prisms: turning through 90° and 180°

For glass, $C\approx 42^{\circ }$, so a ray meeting a face at $45^{\circ }$ inside is totally reflected.

• Deviation of 90°: the ray enters normally through one of the shorter faces, goes straight on, meets the hypotenuse at $i=45^{\circ }>42^{\circ }$, is totally reflected and leaves normally through the other short face, turned through $90^{\circ }$. Used in periscopes.
• Deviation of 180°: the ray enters normally through the hypotenuse, is totally reflected at each short face (each $i=45^{\circ }$), and comes back out through the hypotenuse parallel to its original path but reversed. Used in binoculars and bicycle reflectors; it also inverts the image (erecting prism).

Worked example

Why does a ray entering normally through a short face of a 45°–45°–90° glass prism ($C=42^{\circ }$) undergo TIR at the hypotenuse? What is the deviation?

Try it first, then show the solutionSolution

1. It enters undeviated and meets the hypotenuse at $45^{\circ }$ to the normal.
2. $45^{\circ }>42^{\circ }$, and it is going from glass to air: TIR.
3. It leaves normally through the other short face: deviation $=90^{\circ }$.

Answer: Because 45° > C; deviation 90°

Equilateral and 30°–60°–90° prisms

Equilateral (60°, 60°, 60°) prism: a ray entering normally through one face meets the second face at $i=60^{\circ }>42^{\circ }$: TIR. It then meets the third face normally and emerges undeviated there. The total deviation is $180^{\circ }-2\times 60^{\circ }=60^{\circ }$.

30°–60°–90° prism (angles $A=90^{\circ }$, $B=60^{\circ }$, $C=30^{\circ }$ at the vertices): find the angle of incidence at the hypotenuse with geometry each time.

• Ray entering normally through face $AB$ travels parallel to $AC$ and meets the hypotenuse at $i=60^{\circ }$: TIR.
• Ray entering normally through face $AC$ travels parallel to $AB$ and meets the hypotenuse at $i=30^{\circ }$: it refracts out (no TIR).

Always measure the angle of incidence from the normal, not the surface.

Worked example

A ray falls normally on one face of an equilateral glass prism ($C=42^{\circ }$). Find its angle of incidence on the second face and state what happens.

Try it first, then show the solutionSolution

1. Inside, the ray is perpendicular to the first face; the angle between the first and second faces is $60^{\circ }$.
2. So the ray makes $60^{\circ }$ with the normal to the second face: $i=60^{\circ }$.
3. $60^{\circ }>42^{\circ }$: TIR.

Answer: i = 60°; total internal reflection

TIR prism versus plane mirror

Advantages of a total reflecting prism over a plane mirror (qualitative):

• TIR reflects almost 100% of the light; a mirror absorbs some, so prism images are brighter.
• A prism gives one clear image; a thick glass mirror forms multiple images (partial reflections at the front surface).
• The reflecting surface of a prism does not tarnish; a mirror's silvering fades and peels with time.

This is why periscopes, binoculars and cameras use total reflecting prisms.

Worked example

Give two reasons why a periscope uses right-angled prisms rather than plane mirrors.

Try it first, then show the solutionSolution

1. TIR reflects almost all the light, so the image is brighter.
2. No multiple images and no silvering to tarnish.

Answer: Brighter single image; no tarnishing or multiple images

Applications of total internal reflection

• Sparkling of a diamond: its small critical angle (about $24^{\circ }$) and careful cutting make light undergo TIR many times inside before leaving.
• Optical fibres: light travels along thin glass fibres by repeated TIR at the walls; used in telecommunication and in endoscopes to see inside the body.
• Mirage: on hot days, air near the road is hotter and rarer; light from the sky bends more and more and is finally totally reflected upwards, so the road seems to show water.
• Periscopes and binoculars: right-angled prisms (above).

Worked example

Why does a well-cut diamond sparkle more than a glass imitation of the same shape?

Try it first, then show the solutionSolution

1. Diamond's critical angle (about $24^{\circ }$) is much smaller than glass's (about $42^{\circ }$).
2. So far more rays inside a diamond exceed $C$ and are totally reflected many times before leaving through the top, making it sparkle.

Answer: Its small critical angle causes repeated TIR.

Physics in real life: Total Internal Reflection

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.

Topics in this chapter

• Critical Angle and μ = 1/sin C
• Conditions for Total Internal Reflection
• Total Internal Reflection in Prisms

Total Internal Reflection formula sheet

Critical angle

$\mu =\frac{1}{\sin C}$

μ of the denser medium with respect to air.

Critical angle between two media

$\sin C=\frac{{\mu }_{\text{rarer}}}{{\mu }_{\text{denser}}}$

e.g. glass–water.

Typical critical angles

$C_{\text{glass}}\approx 42^{\circ },C_{\text{water}}\approx 48.6^{\circ },C_{\text{diamond}}\approx 24.4^{\circ }$

For μ = 1.5, 4/3, 2.42.

Conditions for TIR

$\text{denser}\to \text{rarer}\text{and}i>C$

Both needed.

Deviation after one TIR

$\delta =180^{\circ }-2i$

i = angle of incidence at the reflecting face.

Total Internal Reflection: diagrams to practise

Practise each one on paper: draw it from the checklist, then tick off every label.

How the board asks Total Internal Reflection

The question patterns to expect, and the method that works for each.

Tricks to remember Total Internal Reflection

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

• Dense to light, angle past C

  TIR needs: from dense to less dense, and i bigger than C.

  Use it when: Conditions.

• One over sine C

  μ = 1/sin C; glass 1.5 ↔ 42°.

  Use it when: Numericals.

• Bigger μ, smaller C

  Diamond (2.42) has C ≈ 24°; violet has smaller C than red.

  Use it when: Colour and material questions.

• 45 beats 42

  In a 45° prism the inner angle (45°) beats glass's C (42°), so TIR happens.

  Use it when: Right-angled prisms.

Total Internal Reflection: board-level solved questions

Ordered from board level to HOTS. Cover the solution, write your own, then compare step by step.

Case-study practice (Section B style)

Read the situation, then answer every part. In the board paper this is a 10-mark question split into 3 + 3 + 4 marks.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Where students lose marks in Total Internal Reflection

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

• ✗Mistake: Ignoring the direction of travel

  CISCE examiners' comments, 2025: for a ray going from water into glass at 55° (critical angle 54°), candidates concluded that TIR occurs, not noticing that water to glass is rarer to denser.

  ✓Do this: Check 'denser to rarer?' before comparing i with C.

  Usually costs: 2 marks.

• ✗Mistake: Wrong angle at the inner face

  CISCE examiners' comments, 2025: in a prism question candidates confused rays, did not mark the angle of incidence at the new surface, or measured it from the surface instead of the normal.

  ✓Do this: Draw the normal at each inner face and find i by geometry (angles of a triangle, parallel lines).

  Usually costs: 1 to 2 marks.

• ✗Mistake: Misreading prism angles and critical angle

  CISCE examiners' comments, 2024: candidates gave 47° or 133° as the critical angle, assumed an isosceles prism and gave 45° for its angle, or gave 90° or 47°.

  ✓Do this: Work out each angle from the diagram's geometry; the critical angle is the angle of incidence (from the normal) for which r = 90°.

  Usually costs: 1 mark each.

• ✗Mistake: Colour and critical angle

  CISCE examiners' comments, 2024: asked which colour would undergo TIR instead of blue, candidates named any colour or red, not seeing how critical angle depends on wavelength; and for red danger signals they wrote 'refraction' or 'seen from far' instead of least scattering.

  ✓Do this: Violet/blue: larger μ, smaller C, so more easily totally reflected; red: smaller μ, larger C. Red signals: red is scattered least.

  Usually costs: 1 mark each.

• ✗Mistake: Misunderstanding total deviation

  CISCE examiners' comments, 2025: candidates were unclear on the angle of deviation when a ray is totally reflected inside an equilateral prism.

  ✓Do this: Deviation is the angle between the original incident direction and the final emergent direction; for one reflection, δ = 180° − 2i.

  Usually costs: 1 mark.

• ✗Mistake: Missing arrows on rays

  CISCE examiners' comments, 2025: candidates forgot arrows when completing ray paths, or drew the path when the question asked only for the name of the ray.

  ✓Do this: Arrows on every ray; answer exactly what is asked.

  Usually costs: 1 mark.

Practice questions on 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.

1. Q1 · 1 mark · MCQBoard level

   The critical angle for glass of refractive index 1.5 is about:
   (a) 24°
   (b) 42°
   (c) 48°
   (d) 60°

   Hint

   sin C = 1/1.5.

   Answer

   (b)

2. Q2 · 1 mark · MCQBoard level

   To turn a ray through 180° with a 45°–45°–90° prism, the ray must fall normally on:
   (a) one of the short faces
   (b) the hypotenuse face
   (c) the base at 45°
   (d) any face

   Hint

   Two reflections needed.

   Answer

   (b)

3. Q3 · 1 mark · MCQHarder board level

   If the refractive index of a medium increases, its critical angle:
   (a) increases
   (b) decreases
   (c) stays the same
   (d) becomes 90°

   Hint

   sin C = 1/μ.

   Answer

   (b)

4. Q4 · 1 mark · Assertion-reasonBoard level

   Assertion (A): Total internal reflection cannot occur when light goes from air into glass.
   Reason (R): TIR needs light to travel from a denser to a rarer medium.
   (a) (A) is true and (R) is false.
   (b) (A) is false and (R) is true.
   (c) Both (A) and (R) are true, and (R) is the correct explanation for (A).
   (d) Both (A) and (R) are true, but (R) is not the correct explanation for (A).

   Hint

   First condition.

   Answer

   (c)

5. Q5 · 2 marks · Short answerHarder board level

   The critical angle of a medium is 45°. Find its refractive index and the speed of light in it.

   Hint

   μ = 1/sin 45°.

   Answer

   $\mu =\sqrt{2}\approx 1.41$; $V=\frac{3\times 10^8}{\sqrt{2}}\approx 2.12\times 10^8$ m/s.

6. Q6 · 2 marks · Short answerHarder board level

   State two differences between total internal reflection in a prism and reflection from a plane mirror.

   Hint

   Brightness and images.

   Answer

   TIR reflects almost all the light (brighter); a mirror absorbs some. A prism gives one image; a thick mirror gives multiple images (and its silvering can tarnish).

7. Q7 · 3 marks · Long answerBoard level

   (a) Define critical angle. (b) State its relation with refractive index. (c) State the two conditions for total internal reflection.

   Hint

   r = 90°.

   Answer

   (a) The angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°. (b) μ = 1/sin C. (c) Light goes from denser to rarer; i > C.

8. Q8 · 3 marks · Long answerHarder board level

   The refractive index of water is $\frac{4}{3}$. (a) Find its critical angle. (b) A ray from a lamp at the bottom of a pond meets the surface at 50°. What happens? (c) What happens at 45°?

   Hint

   sin C = 0.75.

   Answer

   (a) $C\approx 48.6^{\circ }$. (b) $50^{\circ }>C$: totally reflected back into the water. (c) $45^{\circ }<C$: refracts into the air, bending away from the normal.

9. Q9 · 4 marks · Long answerHOTS / competency

   For a glass prism, ${\mu }_{\text{red}}=1.51$ and ${\mu }_{\text{violet}}=1.53$. (a) Find the critical angle for each colour. (b) A ray of white light meets an inner face at $41^{\circ }$. Which colour is totally reflected and which emerges? Explain.

   Hint

   Compare 41° with each C.

   Answer

   (a) $C_{\text{red}}\approx 41.5^{\circ }$, $C_{\text{violet}}\approx 40.8^{\circ }$. (b) $41^{\circ }>40.8^{\circ }$, so violet is totally reflected; $41^{\circ }<41.5^{\circ }$, so red refracts out. The higher μ of violet gives it a smaller critical angle.

10. Q10 · 3 marks · Long answerHarder board level

    Draw a 45°–45°–90° prism turning a ray through 180°. Explain why the image of an arrow seen through it is inverted, and name one instrument that uses this.

    Hint

    Two reflections swap the order of rays.

    Answer

    Ray enters normally through the hypotenuse, is totally reflected at each short face and returns through the hypotenuse. The two reflections interchange the rays from the two ends of the object, so the image is inverted. Used in binoculars (to erect the image formed by the lenses).

11. Q11 · 1 mark · MCQHOTS / competency

    Compared with the critical angle for a glass–air boundary, the critical angle for a glass–water boundary is:
    (a) smaller
    (b) larger
    (c) the same
    (d) zero

    Hint

    sin C = μ_water/μ_glass.

    Answer

    (b): about 62.7° compared with 42°.

12. Q12 · 4 marks · Long answerHOTS / competency

    Explain, using total internal reflection, (a) why an empty test tube dipped obliquely in water looks silvery, (b) the formation of a mirage, (c) why optical fibres can carry light round bends.

    Hint

    Find the denser and rarer media in each case.

    Answer

    (a) Light in the water meets the glass–air boundary of the empty tube at more than the critical angle and is totally reflected, so the tube shines like a mirror. (b) Air near a hot road is rarer; light from the sky bends away from the normal through the layers until it is totally reflected upwards, giving an image of the sky. (c) Light in the denser core meets the walls at more than C and is reflected again and again along the fibre.

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. 1.Define critical angle.Show answer

   The angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°.

2. 2.Relation between μ and C?Show answer

   μ = 1/sin C

3. 3.Two conditions for TIR?Show answer

   Denser to rarer, and angle of incidence greater than C.

4. 4.Critical angle of glass (μ = 1.5)?Show answer

   About 42°.

5. 5.Deviation by a 45° prism with light entering a short face normally?Show answer

   90°

6. 6.Deviation with light entering the hypotenuse normally?Show answer

   180°

7. 7.Is the critical angle larger for red or violet?Show answer

   Red.

Quick revision checklist

The night before the exam: can you do each of these without looking?

• ☐Can you define critical angle precisely?
• ☐Can you find C from μ and μ from C?
• ☐Do you check denser → rarer first?
• ☐Can you find the angle at an inner face by geometry?
• ☐Can you draw 90° and 180° prism paths with arrows?
• ☐Can you give three advantages of prisms over mirrors?

Total Internal Reflection: frequently asked questions