6. Refraction of Light
Refraction & Everyday Observations
Refraction is the bending (change in direction) of light when it travels obliquely from one transparent medium to another with different optical density (different speed of light).
- Coin appears again when water is poured: Rays bend at water–air surface so they reach your eye.
- Pencil in water looks bent/thicker: Parts of the pencil under water form rays that bend at the surface, shifting the apparent position.
- Glass slab experiment: The emergent ray is parallel to the incident ray but laterally displaced (two refractions cancel direction change but shift the path).
Laws of Refraction (Snell’s Law)
- The incident ray, refracted ray and the normal at the point of incidence all lie in the same plane.
- For a given pair of media, the ratio \( \dfrac{\sin i}{\sin r} \) is a constant:
\[ \frac{\sin i}{\sin r} = n_{21} \]where \(n_{21}\) is the refractive index of medium 2 with respect to medium 1 (Snell’s Law).
Absolute & Relative Indices
\(c\) = speed of light in vacuum; \(v\) = speed in medium; \(n_1,n_2\) are absolute indices.
Bending Rules
- Rarer → Denser: bends towards normal.
- Denser → Rarer: bends away from normal.
- Normal incidence: \(i = 0^\circ \Rightarrow r = 0^\circ\) (no bending).
Refractive Index: Values & Meaning
Typical absolute indices (at standard conditions): Air ≈ 1.0003, Water ≈ 1.33, Crown glass ≈ 1.52, Diamond ≈ 2.42. Higher index ⇒ slower light in that medium.
Atmospheric Refraction: Mirage, Twinkling, Early Sunrise
- Mirage: Hot air near ground is optically rarer than the cooler air above; ray paths curve upward, producing an apparent image below—illusion of water.
- Twinkling of stars: Turbulent layers (varying refractive index) continually change a star’s apparent position and brightness, so it twinkles. Planets don’t (extended sources average out fluctuations).
- Advanced sunrise & delayed sunset: Bending in the atmosphere lets us see the Sun before it actually rises and after it sets.
Dispersion of Light (VIBGYOR)
Different colours (wavelengths) travel at different speeds in a medium ⇒ different refractive indices ⇒ different deviations.
- Order in a prism: Violet (max deviation) → … → Red (min deviation).
- White light splits into a spectrum; recombination with an inverted prism can recover white light.
Total Internal Reflection (TIR) & Critical Angle
When light travels from a denser medium (1) to a rarer medium (2): increase \(i\) ⇒ increase \(r\). At a particular \(i=i_c\), the refracted ray grazes the boundary (\(r=90^\circ\))—this \(i_c\) is the critical angle. For \(i>i_c\), no refraction, only reflection back into the denser medium: Total Internal Reflection.
Here \(n_1 > n_2\) (denser to rarer). Applications: diamonds’ sparkle, optical fibers, mirage, prisms in binoculars.
Rainbow (Nature’s Prism)
Sunlight in raindrops undergoes refraction + dispersion, then internal reflection, then refraction again → circular arc spectrum (primary rainbow).
4. Effects of Electric Current
Energy & Power in a Circuit
- Unit of power: \(1\,\text{W} = 1\,\text{J s}^{-1}\); practical unit: \(1\,\text{kW}\).
- Electric energy: \(1\,\text{kWh} = 3.6\times10^6\,\text{J}\) (one “unit” on bills).
- Heating devices: high-resistivity wires (nichrome) & bulbs (tungsten) use \(I^2R\) heating.
Magnetic Effect of Current
- Straight conductor: Concentric field lines around wire; stronger with more current and closer distance.
- Right-hand thumb rule: Thumb → current, curled fingers → magnetic field direction.
- Loop/Solenoid: Field strengthens with turns; solenoid interior has uniform field and acts like a bar magnet (ends behave as N/S poles).
Force on a Current-Carrying Conductor
In a magnetic field, a current-carrying conductor experiences a force ⟂ to both current and field.
Electric Motor (DC, Split-Ring)
A rectangular coil in a magnetic field carries current; opposite forces on two sides create a torque causing rotation. A split-ring commutator reverses current each half-turn, maintaining continuous rotation.
- Uses: fans, mixers, pumps, washing machines, etc.
Electromagnetic Induction (Faraday)
Changing magnetic flux through a circuit induces an emf/current.
AC & DC; Electric Generator
- AC: Alternates direction; India mains: \(50\,\text{Hz}\).
- DC: Steady in one direction (cells, batteries, DC generator with split-ring commutator).
- AC Generator: Rotating coil in magnetic field with slip rings gives alternating emf; with split ring ⇒ DC output.
Chapter 6 — Refraction of Light: Practice Questions & Perfect Solutions
1) Fill in the blanks & explain
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a) Refractive index depends on the frequency (or colour / wavelength) of light.
Explanation: In a medium, different colours (frequencies) travel with different speeds, so \(n=\dfrac{c}{v}\) varies with frequency (dispersion). Red has the least \(n\) and violet the highest for the same medium.
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b) The change in direction of light rays while going from one medium to another is called refraction.
Explanation: Speed changes at a boundary \((v_1 \to v_2)\), and by Snell’s law the ray bends: \(\dfrac{\sin i}{\sin r}=n_{21}\).
2) Prove the statements
a) For a glass slab, if the angle of incidence is \(i\) and the angle of emergence is \(e\), then \(i=e\).
Proof: Consider a parallel-sided slab (air–glass–air). At first surface:
Inside the slab, the ray meets the second surface with angle of incidence \(i'\). Because the faces are parallel, the internal angles are equal: \(i'=r\).
At the second surface (glass to air):
Substitute \(i'=r\): \(\dfrac{\sin r}{\sin e}=\dfrac{1}{n_{ga}}\). Multiply with the first relation:
With \(0^\circ\le i,e<90^\circ\), this gives \(i=e\). Also, the emergent ray is parallel to the incident ray (lateral shift only).
b) A rainbow is the combined effect of refraction, dispersion, and total internal reflection.
Reasoning:
- Refraction & dispersion at entry: Sunlight enters a raindrop and refracts; different colours deviate differently (dispersion) creating colour separation.
- Total internal reflection: The internal ray reflects off the back surface of the drop (for suitable incidence, beyond critical angle).
- Refraction at exit: Rays refract again when leaving the drop, preserving colour separation and producing bright concentric arcs (primary rainbow).
3) MCQs — choose the correct answer (with reason)
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A. Reason for twinkling of stars?
Answer: (iv) Changing refractive index of the atmospheric gases.
Turbulent layers cause random refraction → apparent position/brightness fluctuates → twinkling.
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B. We can see the Sun even when it is a little below the horizon because of
Answer: (ii) Refraction of light.
Atmospheric refraction bends sunlight along a curved path to the observer → advanced sunrise & delayed sunset.
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C. If \(n_{\text{glass, air}}=\dfrac{3}{2}\), then \(n_{\text{air, glass}}=\ ?\)
Answer: \(\displaystyle \frac{2}{3}\) (reciprocal rule: \(n_{21}=\dfrac{1}{n_{12}}\)).
4) Numerical Examples (step-by-step)
a) Speed of light in a medium is \(1.5\times10^8\ \text{m s}^{-1}\). Find its absolute refractive index.
Result: \(n=2\)
b) If absolute refractive indices are \(n_g=\dfrac{3}{2}\) (glass) and \(n_w=\dfrac{4}{3}\) (water), find \(n_{g,w}\) (glass w.r.t. water).
Result: \(\displaystyle n_{g,w}=\frac{9}{8}\)