Light

Chapter in a nutshell: Light bends (refraction) when its speed changes between media; the bending is governed by the refractive index. A glass slab shifts a ray sideways; a prism deviates and disperses white light into a spectrum. Beyond the critical angle we get total internal reflection. Lenses form images described by the lens formula and magnification, and a lens's converging power is its power in dioptres.

1. Refraction of Light

• Rarer → denser medium: light slows down and bends towards the normal.
• Denser → rarer medium: light speeds up and bends away from the normal.
• A ray along the normal (i = 0) passes undeviated.

Laws of refraction:

1. The incident ray, the refracted ray and the normal all lie in the same plane.
2. Snell's law: $\dfrac{\sin i}{\sin r}=\text{constant}={}_1n_2$ (for a given pair of media and colour of light).

Refractive index (n): $$n=\frac{\sin i}{\sin r}=\frac{\text{speed of light in vacuum }(c)}{\text{speed of light in medium }(v)}$$

• No unit; greater n ⇒ optically denser, light slower.
• Depends on: nature of the medium, and colour (wavelength) of light — n is greatest for violet, least for red.
• Real & apparent depth: an object in water looks raised; $n=\dfrac{\text{real depth}}{\text{apparent depth}}$.

2. Refraction Through a Glass Slab

• Lateral displacement increases with: greater slab thickness, larger angle of incidence, and higher refractive index.

3. Prism: Deviation & Dispersion

• A prism bends a ray towards its base; the angle between the incident and emergent rays is the angle of deviation (δ).
• Dispersion: white light splits into its seven colours (VIBGYOR) on passing through a prism, because each colour has a different refractive index (hence different speed and deviation). Violet deviates most (smallest speed, largest n), red least.
• The band of colours formed is the spectrum. A second inverted prism can recombine them into white light (Newton's experiment).

4. Total Internal Reflection (TIR)

• Critical angle (C): the angle of incidence (in the denser medium) for which the angle of refraction is 90°.

• Two conditions for TIR: (i) light goes from denser to rarer medium; (ii) angle of incidence > critical angle.
• Applications: totally reflecting prisms (periscope, binoculars — give brighter images than mirrors), optical fibres (signal transmission, endoscopy), the mirage, and the sparkle/brilliance of a diamond (small critical angle ≈ 24°).

5. Lenses — Types & Technical Terms

Technical terms:

• Centre of curvature (C₁, C₂): centres of the spheres whose parts form the two surfaces.
• Radius of curvature: radius of those spheres.
• Principal axis: line joining the two centres of curvature.
• Optical centre (O): point on the axis through which a ray passes undeviated (and undisplaced for a thin lens).
• Principal foci (F₁, F₂): a lens has two foci, one on each side; the focal length (f) is the distance from O to the focus.
• Focal length depends on (i) refractive index of the lens material (placing a lens in water increases f), and (ii) radii of curvature.
• Covering half a lens does not change image position/size — only its brightness decreases.

6. Rules for Ray Diagrams (convex lens)

1. A ray parallel to the principal axis passes through the second focus F₂ after refraction.
2. A ray through the optical centre O goes straight (undeviated).
3. A ray through the first focus F₁ emerges parallel to the axis.

7. Image Formation by a Convex Lens

8. Lens Formula, Magnification & Power

• Sign convention (real-is-positive/Cartesian as per text): distances measured against the incident light are negative.
• Magnification m: |m| > 1 enlarged, < 1 diminished; negative m = real/inverted, positive = virtual/erect.
• Power of a lens: $P=\dfrac{1}{f\,(\text{in metres})}$, unit dioptre (D). Convex lens +ve, concave lens −ve. A more powerful lens has a shorter focal length.

9. Uses of Lenses & The Spectrum

• Convex: spectacles for long-sight (hypermetropia), magnifying glass, camera, microscope, telescope objective.
• Concave: spectacles for short-sight (myopia), peep-holes, in lens combinations.
• Spectrum of white light: VIBGYOR. The full electromagnetic spectrum (increasing frequency): radio waves → microwaves → infrared → visible light → ultraviolet → X-rays → gamma rays.

10. Worked Numerical Examples (ICSE pattern)

Q2. The refractive index of glass is 1.5 and speed of light in vacuum is $3\times10^{8}$ m s⁻¹. Find the speed of light in glass. Solution: $v=\dfrac{c}{n}=\dfrac{3\times10^{8}}{1.5}=\mathbf{2\times10^{8}\ m\,s^{-1}}$.

Q3. The critical angle of a medium is 30°. Find its refractive index. Solution: $n=\dfrac{1}{\sin C}=\dfrac{1}{\sin30^\circ}=\dfrac{1}{0.5}=\mathbf{2}$.

Q4. An object is placed 30 cm in front of a convex lens of focal length 10 cm. Find the image distance and magnification. Solution: $u=-30$, $f=+10$: $\dfrac{1}{v}=\dfrac{1}{f}+\dfrac{1}{u}=\dfrac{1}{10}-\dfrac{1}{30}=\dfrac{2}{30}\Rightarrow v=+15$ cm (real). $m=\dfrac{v}{u}=\dfrac{15}{-30}=\mathbf{-0.5}$ (real, inverted, diminished).

Q5. A convex lens has focal length 25 cm. Find its power. Solution: $P=\dfrac{1}{0.25}=\mathbf{+4\ D}$.

Q6. A concave lens has power −2.5 D. Find its focal length. Solution: $f=\dfrac{1}{P}=\dfrac{1}{-2.5}=-0.4\ \text{m}=\mathbf{-40\ cm}$.

11. Key Terms — Quick Glossary

12. Common Mistakes to Avoid

• Saying light "bends towards the normal entering a rarer medium" — it's the opposite (denser → towards normal).
• Forgetting the sign convention in the lens formula.
• Confusing a glass slab's lateral shift (no deviation) with a prism's deviation/dispersion.
• Stating only one condition for TIR — both (denser→rarer and i > C) are needed.
• Writing power in m⁻¹ "per metre" without the unit dioptre; forgetting concave power is negative.

13. Likely Exam Questions (with crisp answers)

1. Define refractive index in two ways. → $\sin i/\sin r$; and $c/v$.
2. Why does a stick in water appear bent? → Refraction at the water surface.
3. State Snell's law. → $\sin i/\sin r$ = constant for a given pair of media.
4. What happens to a ray through a glass slab? → Emerges parallel to the incident ray, laterally displaced.
5. Why does a prism disperse white light? → Different colours have different refractive indices → different deviations.
6. Which colour deviates most through a prism, and why? → Violet — it has the highest refractive index (lowest speed).
7. State the two conditions for TIR. → Denser→rarer medium; angle of incidence > critical angle.
8. Relate refractive index and critical angle. → $n = 1/\sin C$.
9. Give two applications of TIR. → Optical fibres; totally reflecting prisms (periscope/binoculars).
10. Why are reflecting prisms preferred to mirrors in periscopes? → TIR gives brighter images with no silvering to tarnish.
11. Define optical centre. → Point on the axis through which a ray passes undeviated.
12. Distinguish real and virtual focus. → Convex lens: rays actually meet (real); concave lens: rays appear to diverge (virtual).
13. Where must an object be for a convex lens to act as a magnifying glass? → Between the focus F and the lens.
14. Define the power of a lens; its unit. → $P = 1/f$ (m); unit dioptre (D).
15. A convex lens is placed in water — what happens to its focal length? → It increases.
16. Name the image by a concave lens for any object position. → Virtual, erect, diminished (between O and F).

14. Refraction Phenomena in Nature

• Twinkling of stars: continuous refraction through atmospheric layers of varying density.
• A coin in water rises / a pool looks shallower: apparent depth < real depth ($n=$ real/apparent depth).
• Sun seen before sunrise & after sunset: atmospheric refraction bends light over the horizon.
• Mirage (hot desert/road): successive refraction + TIR in layers of hot air make the sky's image look like water.

15. More Worked Numericals

Q8. An object 4 cm tall is placed 20 cm from a convex lens of focal length 10 cm. Find image distance, magnification and image height. Solution: $u=-20,f=+10$: $\dfrac1v=\dfrac1{10}-\dfrac1{20}=\dfrac1{20}\Rightarrow v=+20$ cm. $m=v/u=20/-20=-1$ → image is real, inverted, 4 cm (same size) at 20 cm.

Q9. Two thin lenses of power +5 D and −2 D are in contact. Find the power and focal length of the combination. Solution: $P=P_1+P_2=5-2=\mathbf{+3\,D}$; $f=1/3\,\text{m}=\mathbf{+33.3\,cm}$ (converging).

16. More Exam Questions (with crisp answers)

1. Why do stars twinkle but planets generally don't? → Stars are point sources; atmospheric refraction varies their light; planets are extended sources, averaging out.
2. Why does a swimming pool appear shallower than it is? → Light from the bottom refracts away from the normal at the surface; apparent depth < real depth.
3. A ray strikes a glass slab normally — does it bend? → No (i = 0, so no bending; it passes straight).
4. Define critical angle. → The angle of incidence in the denser medium for which the angle of refraction is 90°.