Refraction of LightClass 10 Science Part 1 Chapter 6 Notes – Maharashtra Board

Summary: Refraction of Light

Dip a pencil in a glass of water and it looks thicker and even broken at the surface. Put a coin in an empty steel vessel, step back till it hides, and pour water in — the coin pops back into view. Both tricks happen because light changes direction when it passes from one transparent medium to another. This bending is called refraction.

Refraction follows two simple laws. The incident ray, the refracted ray and the normal lie in one plane, and for a given pair of media sin i ÷ sin r is always the same number, the refractive index. Light slows down in denser media like glass and water, and that change in speed is the real cause of bending.

Our own atmosphere refracts light too. Layers of hot and cold air create mirages on highways, make things shimmer above a Holi fire, make stars twinkle while planets shine steadily, and even let us see the Sun a little before it actually rises and after it sets.

White sunlight is a mix of colours. A prism slows each colour by a different amount, so the colours spread out into a spectrum from violet to red. This is dispersion. When light inside a denser medium meets the surface at more than the critical angle, it cannot escape and is fully reflected back — total internal reflection.

A rainbow brings all these ideas together. Every raindrop refracts sunlight, splits it into colours, reflects it inside and refracts it again on the way out. Understanding refraction thus explains everything from your spectacles to diamonds sparkling and the colours in the sky after monsoon showers.

Key points to remember

• Refraction is the change in direction of light when it passes from one transparent medium to another.
• Light bends towards the normal when going from a rarer to a denser medium, and away from the normal when going from denser to rarer.
• A ray falling along the normal (i = 0) goes straight without bending (r = 0).
• First law: the incident ray, refracted ray and normal at the point of incidence lie in the same plane, with the two rays on opposite sides of the normal.
• Second law (Snell's law): sin i ÷ sin r = constant = ₁n₂ for a given pair of media.
• In a glass slab, the emergent ray is parallel to the incident ray (e = i) but laterally shifted.
• ₁n₂ = v₁ ÷ v₂; absolute refractive index n = c ÷ v, where c = 3 × 10⁸ m/s.
• ₂n₁ = 1 ÷ ₁n₂, and ₁n₂ × ₂n₃ = ₁n₃.
• Refractive index is different for different media and for different colours in the same medium; diamond has a high value, 2.42.
• Stars twinkle due to continuously changing refractive index of atmospheric air; planets do not twinkle as they are not point sources.
• Due to atmospheric refraction, the Sun is visible a little before actual sunrise and after actual sunset.
• Dispersion: splitting of white light into seven colours (VIBGYOR); violet bends the most, red the least.
• Visible light has wavelengths from about 400 nm (violet) to 700 nm (red); 1 nm = 10^-9 m.
• Total internal reflection occurs when light goes from denser to rarer medium at an angle of incidence greater than the critical angle; a rainbow combines refraction, dispersion and internal reflection.

Refraction of Light – Notes

1. What is refraction?

• Light normally travels in straight lines, which is why opaque objects cast shadows. But at the boundary between two transparent media, it changes direction.
• Refraction of light: the change in direction of light as it passes from one transparent medium into another.
• Pencil in water: the part under water looks thicker, and a slanting pencil looks broken at the water surface, because light from it bends as it leaves water.
• Coin in a vessel: a coin hidden by the rim becomes visible when water is poured in, because light from the coin bends at the water surface and reaches the eye.
• Everyday examples: a swimming pool or a well looks shallower than it is; letters seen through a glass of water look bigger.
• The cause of bending is that light travels at different speeds in different media.

2. Refraction through a glass slab

• Activity: place a rectangular glass slab on paper, trace its outline PQRS, fix pins A and B on a slanting line meeting PQ at N, then from the other side fix pins C and D in line with the images of A and B.
• Join the points: AN is the incident ray, NM is the ray inside the glass, and MD is the emergent ray.
• Refraction happens twice: at N (air to glass, ray bends towards the normal) and at M (glass to air, ray bends away from the normal).
• Angle of refraction r at the first surface equals the angle of incidence i₁ at the second surface (alternate angles, since PQ ∥ SR).
• The angle of emergence e equals the angle of incidence i, because the bending at the two parallel faces is equal and opposite.
• So the emergent ray is parallel to the incident ray but shifted sideways. This sideways shift is called lateral displacement.

3. Laws of refraction

• First law: the incident ray and the refracted ray lie on opposite sides of the normal at the point of incidence, and all three lie in the same plane.
• Second law (Snell's law): for a given pair of media, the ratio sin i ÷ sin r is constant. This constant is the refractive index of the second medium with respect to the first.
• i is the angle between the incident ray and the normal; r is the angle between the refracted ray and the normal.
• Rarer → denser (air to glass): ray bends towards the normal, so r < i.
• Denser → rarer (water to air): ray bends away from the normal, so r > i.
• Normal incidence: a ray along the normal (i = 0) passes straight through (r = 0); there is no bending.

4. Refractive index

• The amount of bending depends on the refractive index of the medium. It is different for different media and for different colours in the same medium.
• Refractive index of medium 2 with respect to medium 1: ₁n₂ = v₁ ÷ v₂ (speed in medium 1 ÷ speed in medium 2).
• Reverse: ₂n₁ = v₂ ÷ v₁ = 1 ÷ ₁n₂.
• Absolute refractive index: refractive index of a medium with respect to vacuum, n = c ÷ v, where c = 3 × 10⁸ m/s. It is always greater than 1 for a material medium.
• Some textbook values: air 1.0003, ice 1.31, water 1.33, kerosene 1.39, crown glass 1.52, dense flint glass 1.66, ruby/sapphire 1.76, diamond 2.42.
• Higher refractive index means light travels slower there; such a medium is optically denser.
• Chain rule: ₁n₂ × ₂n₃ = ₁n₃. Also ₁n₂ = n₂ ÷ n₁ (ratio of absolute indices).

5. Relative refractive index — worked practice

• When both speeds are given, divide the speed in the first medium by the speed in the second.
• When absolute indices are given, divide the index of the second medium by that of the first.
• If the answer is more than 1, the second medium is optically denser than the first; if less than 1, it is rarer.
• Refractive index is a ratio of two speeds, so it has no unit.

6. Atmospheric refraction — mirage, shimmering, twinkling stars, early sunrise

• Hot air is rarer (lower refractive index) than cooler air. The refractive index of air near the ground generally increases as hotter layers give way to cooler ones.
• Mirage: on a hot highway or desert, air near the ground is hottest. Light from a distant object bends gradually upward through these layers and seems to come from below the ground, looking like a pool of water.
• Above a Holi bonfire, the refractive index of the hot, moving air keeps changing, so objects seen through it seem to shake.
• Starlight enters denser and denser air as it comes down, so it keeps bending towards the normal. The star appears higher in the sky than it really is.
• Twinkling: air moves and its temperature and density keep changing, so the refractive index changes all the time. The star's apparent position and brightness flicker. Stars are so far away that they act as point sources.
• Planets are much closer and look like small discs made of many point sources. Their flickers average out, so planets do not twinkle.
• Atmospheric refraction bends sunlight along a curved path, so we see the Sun about two minutes before it actually crosses the horizon at sunrise and a little after it sets.

7. Dispersion of light

• Looking through a transparent plastic scale at light, you can see coloured edges — white light is splitting into colours.
• Light is electromagnetic radiation. Our eyes detect wavelengths from about 400 nm to 700 nm; 1 nm = 10^-9 m.
• Different wavelengths look like different colours: violet (shortest, near 400 nm), indigo, blue, green, yellow, orange, red (longest, near 700 nm).
• In vacuum all colours travel at the same speed, but in glass each colour has a different speed, so the refractive index is different for each colour.
• Dispersion: the separation of white light into its component colours while passing through a medium.
• In a glass prism, violet bends the most and red bends the least, so the colours come out along different paths and form a spectrum. Sir Isaac Newton first used a prism to get the Sun's spectrum.
• A second, inverted prism placed after the first can recombine the colours into white light.
• Glass chandeliers show colours with a tungsten (white) bulb because its light contains all colours.

8. Partial and total internal reflection

• When light goes from a denser medium (water) to a rarer one (air), part of it reflects back into the denser medium (partial reflection) and the rest refracts out.
• Going denser → rarer, the ray bends away from the normal, so r is greater than i. As i increases, r increases too.
• Critical angle (i_c): the angle of incidence in the denser medium for which the angle of refraction is 90°.
• If i is more than the critical angle, no light refracts out; all of it returns into the denser medium. This is total internal reflection.
• Two conditions: light must travel from denser to rarer medium, and i must exceed the critical angle.
• Using Snell's law with r = 90° and sin 90° = 1: sin i_c = ₁n₂ = n₂ ÷ n₁ (medium 1 denser).
• Diamond's small critical angle makes light bounce inside many times, which is why a well-cut diamond sparkles.

9. Rainbow

• A rainbow is usually seen just after rain, with the Sun behind the observer.
• Tiny water droplets in the air act like small prisms.
• Sunlight entering a droplet is refracted and dispersed into colours.
• The coloured light then undergoes internal reflection at the back surface of the droplet.
• On leaving the droplet, it is refracted again, and the colours spread further apart.
• So a rainbow is the combined effect of refraction, dispersion and internal reflection of light. You can make one with a garden hose spray on a sunny morning.

Formulas at a glance

Key terms

Refraction of Light – Flashcards

Read the question, answer it in your head, then tap the card to check. 20 cards.

Refraction of Light – MCQ Quiz

15 questions. Tap an option — you will see at once if it is right and why.

How to study Refraction of Light

⏱ About 3 hours over 3 days

1. Day 1 — Refraction, glass slab and laws
   Try the pencil-in-water and coin-in-vessel activities at home. Draw the glass slab ray diagram with i, r, i₁ and e marked and write the proof that i = e. Write both laws of refraction in your own words and learn the three cases of bending (towards normal, away from normal, no bending).
2. Day 2 — Refractive index and numericals
   Learn n = c ÷ v, ₁n₂ = v₁ ÷ v₂, ₂n₁ = 1 ÷ ₁n₂ and the chain rule. Solve all worked examples here without looking, keeping powers of 10 carefully. Memorise a few table values: water 1.33, crown glass 1.52, diamond 2.42.
3. Day 3 — Atmospheric refraction, dispersion, TIR and rainbow
   Draw the mirage, apparent star position, prism dispersion, total internal reflection and rainbow diagrams. Write 3-mark answers on why stars twinkle but planets don't, and why the Sun is seen before sunrise. Finish with our flashcards and the 15-question quiz.

✍️ Diagrams to practise

• Refraction through a rectangular glass slab (incident, refracted and emergent rays with i, r, e and lateral shift)
• Light ray entering a glass slab from air showing the normal and angles
• Three cases: rarer→denser, denser→rarer, normal incidence
• Mirage over a hot surface
• Apparent position of a star due to atmospheric refraction
• Dispersion of white light by a glass prism (VIBGYOR)
• Partial and total internal reflection with the critical angle
• Formation of a rainbow in a water droplet