Lesson 6: Refraction of Light

Rule 1: Refraction in daily life — Light generally travels in a straight line, so an opaque object makes a shadow. But light changes direction when it goes from one transparent medium to another. A pencil dipped in water looks thicker and broken near the surface, and a coin hidden from view in a vessel becomes visible when water is added.

• Easy : Easy: a pencil looks broken in water because light from the part inside bends when it leaves water.
• Medium : Medium: the bottom of a pond looks shallower than it is, as refraction makes the bottom appear raised.
• Exam-type : Exam: why can we see the hidden coin after pouring water? The rays from the coin bend at the water surface and reach the eye.

Rule 2: The glass slab — In a rectangular glass slab (काचेचा ठोकळा) the first refraction occurs on entering glass from air (angle of incidence i, angle of refraction r) and the second on leaving glass into air (angle of incidence i₁ = r, angle of emergence e = i). The emergent ray is parallel to the incident ray but slightly displaced sideways.

In the figure : In the figure the two refractions in a glass slab.

• Easy : Easy: if the angle of incidence is 40°, the angle of emergence is also 40°, as the emergent ray is parallel to the incident ray.
• Medium : Medium: for a thicker slab the sideways shift (lateral displacement) is larger.
• Exam-type : Exam: name the two refractions in a slab: first from air to glass, second from glass to air; the ray is displaced but not deviated.

Spot the difference

Rule 1: Laws of refraction — First law: the incident ray, the refracted ray and the normal at the point of incidence lie in the same plane; the incident and refracted rays are on opposite sides of the normal. Second law (Snell's law): for a given pair of media, sin i / sin r = constant = n, the refractive index of the second medium with respect to the first. A ray incident along the normal (i = 0) goes ahead without bending (r = 0).

• Easy : Easy: i = 30°, r = 20°. sin 30° = 0.5, sin 20° ≈ 0.34, so n ≈ 0.5 / 0.34 ≈ 1.47.
• Medium : Medium: n = 1.5 and i = 30°. sin r = sin i / n = 0.5 / 1.5 = 0.33, so r ≈ 19.5°.
• Exam-type : Exam: a ray falls along the normal; i = 0, so sin i = 0 and r = 0; the ray goes straight without bending.

In the figure : In the figure the refractive indices of common media.

Rule 2: Refractive index and speed of light — The refractive index depends on the speed of light in the medium: ₁n₂ = v₁ / v₂. The absolute refractive index is with respect to vacuum: n = c / v. Examples: water 1.33, crown glass 1.52, diamond 2.42, air 1.0003. It differs for different colours of light.

• Easy : Easy: if the speed in a medium is 2 × 10⁸ m/s, then n = 3 × 10⁸ / 2 × 10⁸ = 1.5.
• Medium : Medium: speed in water = c / n = 3 × 10⁸ / 1.33 ≈ 2.26 × 10⁸ m/s.
• Exam-type : Exam: in diamond n = 2.42, so v = 3 × 10⁸ / 2.42 ≈ 1.24 × 10⁸ m/s; light is slowest in diamond among these.

Rule 3: Bending towards or away from the normal — Rarer to denser medium: the ray bends towards the normal. Denser to rarer medium: it bends away from the normal. A normally incident ray is not refracted.

In the figure : In the figure rarer to denser and denser to rarer.

• Easy : Easy: air to water: the ray bends towards the normal; water to air: it bends away.
• Medium : Medium: example – speed in a medium is 1.5 × 10⁸ m/s and in vacuum 3 × 10⁸ m/s, so n = 3 / 1.5 = 2.
• Exam-type : Exam: a ray goes from water (n = 1.33) to glass (n = 1.52): glass is denser, so the ray bends towards the normal.

Spot the difference

Rule 1: Mirage — Mirage (मृगजळ): air near a hot road or desert is hot and rarer than the air above, so light rays from a distant object keep changing direction and seem to come from an image inside the ground, giving the illusion of water. Objects beyond a holi fire seem to shake for a similar reason.

In the figure : In the figure a mirage is caused by refraction in hot air.

• Easy : Easy: the 'water' on a hot road is the image of the sky, bent by hot air near the road.
• Medium : Medium: the shaking view above a candle flame or a hot tava is also due to hot air with changing density.
• Exam-type : Exam: a mirage is not real water; it is an optical illusion due to refraction.

Rule 2: Twinkling of stars and sunrise — Twinkling of stars: stars are point sources at very large distances. Air density and refractive index increase towards the ground, so starlight constantly bends towards the normal and the star appears higher than its real position. The changing air density and temperature make its apparent position and brightness keep changing, so the star twinkles. Planets do not twinkle, because they are closer and appear as a collection of point sources, so the average position and brightness stay unchanged. Because of atmospheric refraction we see the Sun a little before it rises above the horizon and for a short while after it sets.

In the figure : In the figure sunrise before the real sunrise.

• Easy : Easy: the Sun looks to be above the horizon about 2 minutes before it is really there.
• Medium : Medium: the day appears about 4 minutes longer (2 minutes at sunrise + 2 at sunset) due to atmospheric refraction.
• Exam-type : Exam: planets do not twinkle because they are close and act as many point sources whose flicker averages out.

Spot the difference

Rule 1: Dispersion and the spectrum — The colours are violet, indigo, blue, green, yellow, orange and red (VIBGYOR). Our eyes are sensitive to wavelengths from 400 nm (violet, the smallest) to 700 nm (red, the largest); 1 nm = 10⁻⁹ m. In vacuum all colours have the same speed, but in a medium the speed depends on the frequency, so the refractive index differs for different colours. Hence white light entering a prism emerges as a spectrum (वर्णपट): red bends the least and violet the most. Sir Isaac Newton was the first to use a glass prism to obtain the Sun's spectrum.

In the figure : In the figure dispersion by a prism.

• Easy : Easy: the order from the top of the spectrum – red at the top (least bent), violet at the bottom (most bent).
• Medium : Medium: 400 nm = 400 × 10⁻⁹ m = 4 × 10⁻⁷ m; 700 nm = 7 × 10⁻⁷ m.
• Exam-type : Exam: why does a prism split white light? Each colour has a different refractive index, so each colour bends by a different angle.

Spot the difference

Rule 1: Critical angle — Light going from a denser to a rarer medium is partly reflected (partial reflection) and partly refracted away from the normal. As i increases, r increases; for a certain i, r becomes 90°. This i is the critical angle (क्रांतिक कोन). For angles of incidence larger than the critical angle, all the light returns to the denser medium: total internal reflection. At the critical angle n = sin i / sin 90° = sin i.

In the figure : In the figure total internal reflection.

• Easy : Easy: for glass with n = 1.5, sin c = 1/1.5 = 0.667, so the critical angle c ≈ 42°.
• Medium : Medium: for water with n = 1.33, sin c = 1/1.33 = 0.75, so c ≈ 49°; for diamond n = 2.42, sin c = 0.41, so c ≈ 24°.
• Exam-type : Exam: conditions for total internal reflection – light goes from denser to rarer medium, and the angle of incidence is more than the critical angle.

Rule 2: The rainbow — A rainbow (इंद्रधनुष्य) is seen mainly after rainfall. Water droplets act as small prisms: light is refracted and dispersed on entering, undergoes internal reflection, and is refracted again on leaving. A rainbow is the combined effect of dispersion, refraction and total internal reflection.

In the figure : In the figure how a rainbow forms.

• Easy : Easy: we see a rainbow when the Sun is behind us and rain drops are in front.
• Medium : Medium: red is on the outside and violet on the inside of the main rainbow.
• Exam-type : Exam: name the three phenomena in a rainbow: refraction, dispersion and total internal reflection.

Spot the difference