Refraction of Light Class 10 Notes, Formulas, Questions | SSC
On this page
This chapter explains why light changes its direction when it passes from one transparent medium into another. It covers the path of light through a glass slab, the two laws of refraction (including Snell's law) and the idea of refractive index linked to the speed of light. It then applies these ideas to everyday effects such as mirages, twinkling of stars, early sunrise and late sunset, dispersion of white light by a prism, total internal reflection and the formation of a rainbow.
Summary
Light normally travels in a straight line, but it bends when it goes from one transparent medium to another. A pencil dipped in water looks thicker and appears broken at the surface, and a coin hidden by the edge of a vessel becomes visible when water is poured in. Both effects happen because light changes direction while coming out of water. This change in the direction of light when it passes from one transparent medium to another is called refraction of light.
When a ray passes through a rectangular glass slab, it is refracted twice: once on entering the glass from air and again on leaving the glass into air. The angle of refraction at the first surface equals the angle of incidence at the second surface, and the angle of emergence equals the angle of incidence (i = e). Since the two faces are parallel, the bending at the two faces is equal and opposite, so the emergent ray is parallel to the incident ray but slightly shifted sideways.
Refraction obeys two laws. First, the incident ray and the refracted ray lie on opposite sides of the normal at the point of incidence, and the incident ray, refracted ray and normal all lie in the same plane. Second, for a given pair of media the ratio sin i / sin r is a constant; this is Snell's law and the constant is the refractive index of the second medium with respect to the first. A ray falling along the normal (i = 0) goes straight without bending (r = 0).
Refractive index depends on the velocity of light in the media. The refractive index of medium 2 with respect to medium 1 equals the speed of light in medium 1 divided by the speed of light in medium 2. The refractive index of a medium with respect to vacuum is its absolute refractive index, for example water 1.33, crown glass 1.52 and diamond 2.42. Light bends towards the normal when it goes from a rarer to a denser medium, away from the normal when it goes from a denser to a rarer medium, and does not bend when it falls normally on the boundary.
Changes in the refractive index of air cause several natural effects. Over a hot road or desert, the air near the ground is hotter and rarer, so light from distant objects bends and appears to come from an image below the ground: this is a mirage. Objects seen through the hot air above a holi fire seem to shake. Starlight bends towards the normal as it enters denser lower layers of the atmosphere, so stars look higher than they are; because the air keeps moving and its density and temperature keep changing, the position and brightness of a star keep changing and it twinkles. Planets are closer and act as a collection of point sources, so their average position and brightness stay steady and they do not twinkle. Atmospheric refraction also lets us see the Sun a little before actual sunrise and a little after actual sunset.
White light is made of colours: violet, indigo, blue, green, yellow, orange and red. Our eyes are sensitive to wavelengths between about 400 nm (violet) and 700 nm (red). In vacuum all colours travel at the same speed, but in a medium their speeds differ, so the refractive index is different for different colours. Hence when white light enters a prism, each colour bends by a different angle (red least, violet most) and a spectrum is formed. The separation of light into its component colours while passing through a medium is called dispersion. Sir Isaac Newton was the first to obtain the spectrum of sunlight using a glass prism.
When light goes from a denser to a rarer medium, part of it is reflected back into the denser medium (partial reflection) and the rest is refracted away from the normal. As the angle of incidence increases, the angle of refraction increases; the angle of incidence for which the angle of refraction becomes 90 degrees is the critical angle. For angles of incidence greater than the critical angle, no light is refracted and all of it is reflected back into the denser medium: this is total internal reflection. A rainbow is produced when sunlight enters tiny raindrops, gets refracted and dispersed, is internally reflected inside the drop and is refracted again while coming out; it is the combined effect of refraction, dispersion and total internal reflection.
Mind map
Refraction of Light
- Basic idea
- Bending of light between two transparent media
- Pencil in water looks broken
- Coin in vessel appears on adding water
- Glass slab
- Two refractions
- i = e
- Emergent ray parallel to incident ray
- Lateral shift
- Laws of refraction
- Incident ray, refracted ray, normal in one plane
- Snell's law: sin i / sin r = constant
- Normal incidence: no bending
- Refractive index
- 1n2 = v1 / v2
- Absolute refractive index n = c / v
- Rarer to denser: towards normal
- Denser to rarer: away from normal
- Atmospheric refraction
- Mirage
- Shaking objects above fire
- Twinkling of stars
- Planets do not twinkle
- Early sunrise, late sunset
- Dispersion
- VIBGYOR
- 400 nm to 700 nm
- Red bends least, violet most
- Newton and the prism
- Total internal reflection
- Partial reflection
- Critical angle: r = 90 degrees
- i greater than critical angle
- Rainbow
Path of a light ray through a glass slab
- Ray AN in air falls on face PQ of the slab at angle of incidence i.
- At N light enters a denser medium (glass), so it bends towards the normal; angle of refraction is r.
- The refracted ray NM travels in a straight line inside the glass to the opposite face SR.
- At M the angle of incidence is i1, and i1 = r because the faces are parallel.
- Light goes from glass into air (denser to rarer) and bends away from the normal; the angle of emergence is e.
- Since the bending at both faces is equal and opposite, e = i.
- The emergent ray MD is parallel to the incident ray AN but displaced sideways.
Important definitions
| Term | Meaning |
|---|---|
| Refraction of light | The change in the direction of light when it passes from one transparent medium into another. |
| Angle of incidence (i) | The angle between the incident ray and the normal at the point of incidence. |
| Angle of refraction (r) | The angle between the refracted ray and the normal at the point of incidence. |
| Snell's law | For a given pair of media, the ratio of sin i to sin r is a constant. |
| Refractive index | The constant sin i / sin r for a pair of media; also equal to the ratio of the speed of light in the first medium to that in the second. |
| Absolute refractive index | The refractive index of a medium with respect to vacuum. |
| Mirage | An optical illusion, seen over hot roads or deserts, in which light from a distant object appears to come from its image inside the ground, due to refraction in layers of air of different density. |
| Dispersion of light | The separation of white light into its component colours while passing through a medium. |
| Spectrum | The band of seven colours (violet to red) obtained by dispersion of white light. |
| Partial reflection | Reflection of part of the light back into the denser medium when light travels from a denser to a rarer medium. |
| Critical angle | The angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90 degrees. |
| Total internal reflection | Reflection of all the light back into the denser medium when the angle of incidence is greater than the critical angle. |
Formulas
| Formula | Meaning |
|---|---|
| \( \frac{\sin i}{\sin r} = n \) | Snell's law: i is the angle of incidence, r the angle of refraction, n the refractive index of the second medium with respect to the first (no unit). |
| \( {}_1n_2 = \frac{v_1}{v_2} \) | Refractive index of medium 2 with respect to medium 1; v1 and v2 are the speeds of light (m/s) in medium 1 and medium 2. |
| \( {}_2n_1 = \frac{v_2}{v_1} = \frac{1}{{}_1n_2} \) | Refractive index of medium 1 with respect to medium 2 is the reciprocal of 1n2. |
| \( n = \frac{c}{v} \) | Absolute refractive index; c = 3 x 10^8 m/s is the speed of light in vacuum and v is the speed in the medium. |
| \( {}_1n_3 = {}_1n_2 \times {}_2n_3 \) | Refractive index of medium 3 with respect to medium 1, obtained from the two intermediate refractive indices. |
| \( {}_1n_2 = \frac{\sin i_c}{\sin 90^\circ} = \sin i_c \) | Critical angle condition when light goes from denser medium 1 to rarer medium 2; ic is the critical angle. |
| \( 1\,\text{nm} = 10^{-9}\,\text{m} \) | Unit used for wavelengths of visible light (about 400 nm to 700 nm). |
Key points to remember
- Light bends only when it passes obliquely from one transparent medium to another; a ray along the normal goes straight.
- In a glass slab, angle of incidence equals angle of emergence (i = e) and the emergent ray is parallel to the incident ray but laterally displaced.
- Rarer to denser: the ray bends towards the normal. Denser to rarer: the ray bends away from the normal.
- Refractive index has no unit; it depends on the speed of light in the media and also on the colour of light.
- Absolute refractive index of air is about 1.0003, water 1.33, crown glass 1.52 and diamond 2.42 (textbook table).
- Stars twinkle because the refractive index of the atmosphere keeps changing; planets do not twinkle because they are nearer and act as extended sources.
- The Sun is visible slightly before sunrise and slightly after sunset because of atmospheric refraction.
- Visible light ranges from about 400 nm (violet) to 700 nm (red); red bends least and violet bends most in a prism.
- Total internal reflection happens only when light travels from a denser to a rarer medium and the angle of incidence exceeds the critical angle.
- A rainbow is the combined effect of refraction, dispersion and total internal reflection in water droplets.
Solved examples
Example 1. Light travels with a velocity of 1.5 x 10^8 m/s in a medium. On entering a second medium its velocity becomes 0.75 x 10^8 m/s. What is the refractive index of the second medium with respect to the first?
Given: v1 = 1.5 x 10^8 m/s, v2 = 0.75 x 10^8 m/s.
Refractive index of medium 2 with respect to medium 1 = v1 / v2.
= (1.5 x 10^8) / (0.75 x 10^8) = 2.
Answer: The refractive index is 2 (no unit).
Example 2. If the speed of light in a medium is 1.5 x 10^8 m/s, what is the absolute refractive index of the medium? (c = 3 x 10^8 m/s)
Absolute refractive index n = c / v.
n = (3 x 10^8) / (1.5 x 10^8) = 2.
Answer: n = 2.
Example 3. The absolute refractive index of water is 1.33. Find the speed of light in water. (c = 3 x 10^8 m/s)
n = c / v, so v = c / n.
v = (3 x 10^8) / 1.33 = 2.26 x 10^8 m/s (approximately).
Answer: Light travels at about 2.26 x 10^8 m/s in water.
Example 4. The absolute refractive indices of glass and water are 3/2 and 4/3 respectively. Find the refractive index of glass with respect to water.
Refractive index of glass with respect to water = (absolute refractive index of glass) / (absolute refractive index of water).
= (3/2) / (4/3) = (3/2) x (3/4) = 9/8.
Answer: 9/8 (= 1.125).
Example 5. The refractive index of glass with respect to air is 3/2. What is the refractive index of air with respect to glass?
Refractive index of air with respect to glass is the reciprocal of that of glass with respect to air.
= 1 / (3/2) = 2/3.
Answer: 2/3.
Example 6. A ray of light passes from air into glass. The angle of incidence is 30 degrees and the refractive index of glass with respect to air is 1.5. Find sin r.
By Snell's law, sin i / sin r = n.
sin r = sin i / n = sin 30 / 1.5 = 0.5 / 1.5 = 0.333.
So r is about 19.5 degrees, which is smaller than i, showing that the ray bends towards the normal on entering the denser glass.
Important questions and answers
Q1. Fill in the blank: Refractive index depends on the ______ of light.
velocity. The refractive index of medium 2 with respect to medium 1 is the ratio of the speed of light in medium 1 to the speed in medium 2, so it depends on the velocity of light in the media.
Q2. Fill in the blank: The change in ______ of light rays while going from one medium to another is called refraction.
direction. Light bends, that is, its direction changes, when it passes obliquely from one transparent medium into another.
Q3. What is the reason for the twinkling of stars? (i) explosions in stars (ii) absorption of light in the atmosphere (iii) motion of stars (iv) changing refractive index of atmospheric gases
(iv) Changing refractive index of the atmospheric gases.
Q4. We can see the Sun even when it is a little below the horizon because of (i) reflection (ii) refraction (iii) dispersion (iv) absorption of light.
(ii) Refraction of light by the earth's atmosphere, which bends the Sun's rays along a curved path towards us.
Q5. State the laws of refraction of light.
1. The incident ray and the refracted ray lie on opposite sides of the normal at the point of incidence, and the incident ray, refracted ray and normal lie in the same plane.
2. For a given pair of media, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant (sin i / sin r = n). This is Snell's law.
Q6. Prove that for a ray passing through a glass slab, the angle of incidence i equals the angle of emergence e.
At the first face (air to glass), sin i / sin r = n, where n is the refractive index of glass with respect to air.
Inside the slab the faces are parallel, so the angle of incidence at the second face i1 = r (alternate angles).
At the second face (glass to air), sin i1 / sin e = 1/n.
Multiplying the two relations: (sin i / sin r) x (sin r / sin e) = n x (1/n) = 1, so sin i = sin e.
Therefore i = e, and the emergent ray is parallel to the incident ray.
Q7. Explain why stars twinkle but planets do not.
Stars are very far away and behave like point sources. Starlight passes through layers of air whose density, temperature and hence refractive index keep changing because the air is in motion. So the apparent position and brightness of a star change continuously and it twinkles.
Planets are much closer and behave like a collection of point sources. The changes in individual points average out, so the average position and total brightness stay the same and planets do not twinkle.
Q8. Explain how a mirage is formed.
On a hot road or in a desert, the air close to the ground is hot and rarer, while the air above it is cooler and denser, so the refractive index increases with height. Light from a distant object bends gradually as it passes through these layers, following the laws of refraction. The rays reach the eye as if coming from below the ground, so the object appears to have an image inside the ground, which looks like a pool of water. This illusion is a mirage.
Q9. What is dispersion of light? Why does a prism produce a spectrum?
Dispersion is the separation of white light into its component colours while passing through a medium. In vacuum all colours travel with the same speed, but in glass the speed depends on the frequency of light. So the refractive index of glass is different for different colours, and each colour bends through a different angle (red least, violet most). The colours come out along different paths and form a spectrum of seven colours.
Q10. What is total internal reflection? State the conditions for it.
When light travels from a denser to a rarer medium at an angle of incidence greater than the critical angle, it is not refracted at all; it is entirely reflected back into the denser medium. This is total internal reflection.
Conditions: (1) light must go from a denser medium to a rarer medium; (2) the angle of incidence must be greater than the critical angle.
Q11. Explain how a rainbow is formed.
After rainfall, many tiny water droplets in the air act like small prisms. Sunlight entering a droplet is refracted and dispersed into colours. The light is then internally reflected at the back of the droplet and is refracted again as it comes out. The combined effect of refraction, dispersion and total internal reflection produces the rainbow.
Q12. Distinguish between light going from a rarer to a denser medium and from a denser to a rarer medium.
Rarer to denser (e.g. air to glass): the ray bends towards the normal, angle of refraction is less than angle of incidence, speed of light decreases, total internal reflection cannot occur.
Denser to rarer (e.g. water to air): the ray bends away from the normal, angle of refraction is greater than angle of incidence, speed of light increases, total internal reflection can occur beyond the critical angle.
Exam tips
- Always draw the normal as a dotted line and mark i, r and e clearly in ray diagrams of the glass slab.
- Write the notation carefully: 1n2 means refractive index of medium 2 with respect to medium 1 and equals v1 / v2.
- In numericals, write the formula first, then substitute with units; refractive index itself has no unit.
- For "give reasons" questions on twinkling, mirage or sunrise, always mention the changing refractive index of air.
- Remember the order of colours VIBGYOR and that red has the longest wavelength (about 700 nm) and bends least.
FAQs
Does refractive index have a unit?
No. It is a ratio of two speeds (or of two sines), so it is a pure number.
Why is the refractive index different for different colours?
In a medium, the speed of light depends on its frequency, so each colour travels at a different speed and has a different refractive index. This is why dispersion occurs.
Is total internal reflection possible when light goes from air into water?
No. It occurs only when light travels from a denser medium to a rarer medium and the angle of incidence is greater than the critical angle.
Which topics of this chapter are most important for the board exam?
Laws of refraction, refractive index numericals, the glass slab proof i = e, twinkling of stars, dispersion by a prism, total internal reflection and the rainbow.
These notes were prepared with AI help from the Balbharati Science and Technology Part 1 textbook (2026-27) and checked against it.
More in Science & Technology Part 1
See all →- Gravitation Class 10 Notes, Formulas, Questions | SSC Gravitation Class 10 SSC notes: Kepler's laws, Newton's law, g and its variation, mass and weight, free fall, escape velocity and solved pro...
- Periodic Classification Class 10 Notes, Formulas, Questions | SSC Periodic Classification Class 10 SSC notes: Dobereiner, Newlands, Mendeleev, modern periodic table, periodic trends and solved questions.
- Chemical Reactions Class 10 Notes, Formulas, Questions | SSC Chemical Reactions and Equations Class 10 SSC notes: writing and balancing equations, reaction types, rate of reaction, redox, corrosion and...
- Effects of Electric Current Class 10 Notes, Formulas | SSC Effects of Electric Current Class 10 SSC notes: Joule's law, power, kWh, fuse, magnetic field, Fleming's rules, motor, induction, AC and DC...
- Heat Class 10 Notes, Formulas, Questions | SSC Heat Class 10 SSC notes: latent heat, regelation, anomalous behaviour of water, Hope's apparatus, dew point, humidity, specific heat, proble...
- Lenses Class 10 Notes, Formulas, Questions | SSC SSC Class 10 Science Part 1 Lenses notes: convex and concave lens images, sign convention, lens formula, power, human eye, defects of vision...