When light crosses from one medium into another, it bends — this single idea, called refraction, explains everything from a bent pencil in a glass to how your eye sees. In this Cavalier lesson you will master Snell's law, refractive index, total internal reflection and the lens formula the NDA exam tests every year.
Why Refraction Shows Up Every Year
Optics is one of the most scoring chapters in NDA General Studies (Physics). Out of the light section, refraction and lenses alone supply several questions per paper — some purely factual ("which lens is used in a magnifying glass?") and some short numericals on the lens formula.
The good news: the concepts are visual and the formulas are few. If you understand why light bends and remember three formulas, you can answer almost anything they throw at you. Most students lose marks here not because the chapter is hard, but because they confuse refraction with reflection or get the sign convention wrong. We will fix both problems in this lesson.
Refraction is also the foundation of many higher topics — dispersion, the rainbow, optical instruments, and the working of the human eye. So time invested here pays off across the whole optics syllabus, and even in some General Knowledge questions about telescopes, microscopes and cameras.
Reflection is light bouncing back; refraction is light bending as it enters a new medium. Don't mix the two — examiners love this confusion.
What Exactly Is Refraction?
Refraction is the bending of a ray of light when it travels from one transparent medium to another because its speed changes. Light moves fastest in vacuum (about 3 × 108 m/s) and slows down in glass or water.
Think of a marching band walking from a hard road onto soft sand at an angle — one side slows first, so the line turns. Light does the same: the part of the wavefront entering the slower medium first lags behind, so the whole ray pivots.
One crucial fact for the exam: during refraction the frequency (colour) of light does not change. Only the speed and wavelength change. This is why a red object stays red whether you view it through air or water — frequency is fixed by the source, not the medium.
Optically denser vs rarer
- A medium where light travels slower is optically denser (e.g. glass).
- A medium where light travels faster is optically rarer (e.g. air).
Going from rarer → denser, the ray bends towards the normal. Going denser → rarer, it bends away from the normal.
The Two Laws of Refraction
Every refraction problem obeys two laws. Memorise them word-perfect.
- First law: The incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane.
- Second law (Snell's law): The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a given pair of media.
Snell's law: sin i ÷ sin r = constant = 1n2, the refractive index of medium 2 with respect to medium 1.
Here i is the angle of incidence and r the angle of refraction, both measured from the normal (not the surface).
Refractive Index — the Heart of It All
The refractive index (n) of a medium tells you how much it slows light down compared with vacuum.
n = speed of light in vacuum (c) ÷ speed of light in medium (v)
Because c is the largest possible speed, n ≥ 1 always.
Some standard values to memorise
- Vacuum / air ≈ 1.00
- Water = 1.33
- Glass = 1.5 (about)
- Diamond = 2.42 (highest common value)
A higher n means light slows down more and bends more sharply. Diamond's huge refractive index is why it sparkles — light gets trapped and bounces inside before escaping.
Refractive index also depends slightly on the colour of light: it is larger for violet than for red. That tiny difference is exactly what splits white light into a spectrum through a prism. For NDA, just remember the ordering of standard values above and the fact that denser media have higher n.
If asked "in which medium does light travel slowest?", pick the one with the highest refractive index. Among air, water, glass and diamond, the answer is diamond.
Relative Refractive Index and Speed
The refractive index of medium 2 with respect to medium 1 links both speeds:
1n2 = v1 ÷ v2 = n2 ÷ n1
So if you know the absolute indices of two media, the relative index is just their ratio. For example, the refractive index of glass (1.5) with respect to water (1.33) is 1.5 ÷ 1.33 ≈ 1.13.
Students flip the ratio. Remember the medium of incidence is on the bottom: 1n2 = n2/n1, light going from 1 into 2.
Total Internal Reflection & the Critical Angle
When light travels from a denser to a rarer medium and the angle of incidence keeps increasing, the refracted ray bends more and more away from the normal. At one special angle it grazes the surface (r = 90°). This angle of incidence is the critical angle (C).
Beyond the critical angle, no light escapes — it is totally reflected back into the denser medium. This is total internal reflection (TIR).
sin C = 1 ÷ n, where n is the refractive index of the denser medium with respect to the rarer one.
Where TIR is used
- Optical fibres — signals travel by repeated total internal reflection.
- Diamonds — brilliant sparkle from trapped light.
- Mirage on hot roads — layers of hot, less-dense air bend light upward.
- Prismatic binoculars and periscopes.
Two conditions for TIR: (1) light must go from denser to rarer, and (2) the angle of incidence must exceed the critical angle.
Lenses: Convex and Concave
A lens is a piece of transparent material bounded by two surfaces, at least one of which is curved. Lenses work entirely by refraction: as light enters and leaves the curved glass it bends twice, and the combined effect either gathers the rays together or spreads them apart. There are two main types.
Convex (converging) lens
- Thicker in the middle, thin at the edges.
- Converges parallel rays to a point — the focus.
- Forms real images (and a virtual one when the object is very close).
- Used in magnifying glasses, cameras, the human eye, and to correct hypermetropia (long-sightedness).
Concave (diverging) lens
- Thinner in the middle, thick at the edges.
- Diverges parallel rays; they appear to spread from a focus.
- Always forms a virtual, erect, diminished image.
- Used to correct myopia (short-sightedness).
Quick recall: Convex corrects hypermetropia; Concave corrects myopia. Both words start with the same letter — an easy memory hook. A magnifying glass, the objective of a camera and the lens of a simple microscope are all convex.
Key Lens Terms and Sign Convention
Before any numerical, fix these terms in your head.
- Optical centre (O): the central point of the lens; rays through it pass undeviated.
- Principal axis: the line through both centres of curvature.
- Focus (F): where parallel rays meet (convex) or appear to meet (concave).
- Focal length (f): distance from optical centre to focus.
Sign convention: distances measured in the direction of incident light are positive, against it negative. For a convex lens f is +ve; for a concave lens f is −ve.
Power of a lens
The power (P) measures how strongly a lens bends light.
P = 1 ÷ f (f in metres). Unit: dioptre (D). Convex power is positive, concave power is negative.
The Lens Formula and Magnification
These two formulas solve almost every lens numerical in NDA.
Lens formula: 1/v − 1/u = 1/f
Magnification: m = v / u = h′ / h
where u = object distance, v = image distance, h = object height, h′ = image height.
A positive magnification means the image is erect and virtual; a negative magnification means the image is inverted and real. If |m| > 1 the image is enlarged, if |m| < 1 it is diminished, and if |m| = 1 it is the same size.
For a single convex lens, the nature of the image depends on where the object sits relative to the focus and twice the focal length (2F). An object beyond 2F gives a small, real, inverted image; at 2F an equal-size real image; between F and 2F an enlarged real image; and inside F a magnified virtual image — which is how a magnifying glass works. A concave lens, by contrast, always gives a diminished virtual erect image, no matter where the object is placed.
The lens formula uses 1/v − 1/u, but the mirror formula uses 1/v + 1/u. Apply the wrong one and your sign collapses. Keep them separate.
Worked Example: Finding the Image
Let's apply the lens formula to a typical convex-lens problem.
An object is placed 30 cm from a convex lens of focal length 20 cm. Find the image distance and magnification.
The image is real, inverted, and twice the size of the object (m = −2). The positive v confirms it forms on the opposite side of the lens from the object.
Always write the sign of every quantity before substituting. Nearly all lens errors are sign errors, not arithmetic.
Refraction in Everyday Life and the Eye
NDA often tests applications rather than maths. Keep these ready.
- Bent straw / shallow pool: light from the object bends as it leaves water, so the object appears raised.
- Twinkling stars: atmospheric layers of varying density refract starlight continuously.
- Sun visible before sunrise: atmospheric refraction lifts the image of the Sun.
- Splitting of white light by a prism: different colours refract by different amounts (dispersion); red bends least, violet most.
- Rainbow: raindrops refract, disperse and internally reflect sunlight, fanning it into seven colours.
- Lemon in a glass of water looking larger — the water acts like a crude lens.
Each of these is just refraction wearing a different costume. If a question describes light "appearing to come from a different position", the cause is almost always atmospheric or medium refraction.
The human eye
The eye's convex lens focuses light on the retina. Its focal length is adjusted by the ciliary muscles — a process called accommodation. Defects and their cures:
- Myopia (near-sighted) → concave lens.
- Hypermetropia (far-sighted) → convex lens.
- Presbyopia (age-related) → bifocal lenses.
Previous-Year Question and 60-Second Recap
Q. The phenomenon by which light bends while passing from one medium to another is called, and the splitting of white light into colours by a prism is called, respectively:
Answer: Refraction and dispersion. Light bends because its speed changes between media (refraction); a prism separates colours because each colour refracts by a different amount (dispersion), with violet bending the most and red the least.
- Refraction = bending of light due to a change in speed between media.
- Snell's law: sin i / sin r = constant = refractive index.
- n = c/v, always ≥ 1; diamond highest (2.42), water 1.33.
- TIR happens denser → rarer beyond the critical angle; sin C = 1/n.
- Convex converges (f +ve); concave diverges (f −ve).
- Lens formula: 1/v − 1/u = 1/f; magnification m = v/u.
- Power P = 1/f in dioptres.
Frequently asked questions
What is the difference between reflection and refraction?
Reflection is light bouncing back from a surface, obeying the law that the angle of incidence equals the angle of reflection. Refraction is light bending as it passes into a new medium because its speed changes.
Why does a refractive index never go below 1?
Refractive index n = c/v, where c is the speed of light in vacuum and v its speed in the medium. Since nothing travels faster than light in vacuum, v can never exceed c, so n is always 1 or greater.
Which lens is used to correct myopia and which for hypermetropia?
A concave (diverging) lens corrects myopia or short-sightedness, while a convex (converging) lens corrects hypermetropia or long-sightedness.
What are the two conditions for total internal reflection?
First, light must travel from a denser medium to a rarer medium. Second, the angle of incidence must be greater than the critical angle for that pair of media.
What is the SI unit of the power of a lens?
The power of a lens is measured in dioptres (D). It equals the reciprocal of the focal length in metres, so a lens of focal length 0.5 m has a power of 2 D.
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