Refraction — Set 3

Correct Answer: A. 19 degrees

• **19 degrees** = apply Snell's law: sin r = sin i / n = sin 30° / 1.5 = 0.5 / 1.5 = 0.333; r = arcsin(0.333) ≈ 19°. • **n = 1.5** — the ray bends towards the normal on entering glass, so r < i; the result of 19° < 30° is consistent with light entering a denser medium. • 💡 Wrong-option analysis: 45 degrees: sin 45° = 0.707, giving n = sin30/sin45 = 0.707 — less than 1, which would mean air is denser than glass — incorrect; 30 degrees: r = i = 30° only when both media have the same refractive index (n1 = n2), meaning no refraction at all; 60 degrees: r > i = 30° would imply the ray bends away from the normal, which happens going from denser to rarer medium, not air to glass.

Correct Answer: B. 42 degrees

• **42 degrees** = use sin c = 1/n for glass (n = 1.5) to air; sin c = 1/1.5 = 0.667; c = arcsin(0.667) ≈ 42°. • **Total internal reflection** — for any angle of incidence greater than 42° inside glass, no refracted ray can exist and light is totally internally reflected; this is exploited in optical fibres and diamond cutting. • 💡 Wrong-option analysis: 60 degrees: sin 60° = 0.866 would require n = 1/0.866 ≈ 1.15, not 1.5; 60° is the critical angle for a less dense glass; 30 degrees: sin 30° = 0.5 would require n = 1/0.5 = 2.0, corresponding to a much denser medium like diamond; 90 degrees: 90° would require n = 1/sin90° = 1, meaning no boundary — the critical angle cannot be 90°.

Correct Answer: A. 42 degrees

• **42 degrees** = apply Snell's law: n_water sin i = n_air sin r; 1.33 × sin 30° = 1.0 × sin r; sin r = 1.33 × 0.5 = 0.665; r = arcsin(0.665) ≈ 42°. • **Denser to rarer** — going from water to air, the ray bends away from the normal, so r > i; 42° > 30° is consistent; the critical angle of water is about 49°, so 30° is below it and normal refraction occurs. • 💡 Wrong-option analysis: 30 degrees: r = i = 30° would mean both media have the same refractive index (no refraction); water has n = 1.33 ≠ 1.0 so refraction must occur; 60 degrees: sin 60° = 0.866, giving n_water = 0.866/0.5 = 1.73 — too high for water; 22 degrees: r = 22° < i = 30° would imply the ray bends towards the normal, meaning the medium entered (air) is denser — air is rarer than water, so bending is away.

Correct Answer: B. 2.0 m

• **2.0 m** = use apparent depth = real depth / n = 3.0 / 1.5 = 2.0 m. • **n = real / apparent** — the pond bottom appears 1.0 m shallower than it really is; this is why pools look shallower than they are, a practical safety concern. • 💡 Wrong-option analysis: 4.5 m: 4.5 = 3.0 × 1.5 — this multiplies real depth by n instead of dividing; it would apply if the observer were inside the denser medium looking out; 2.5 m: 2.5 = 3.0 / 1.2 — uses the wrong refractive index; 3.0 m: equal apparent and real depth would occur only if n = 1 (same medium), i.e. no refraction.

Correct Answer: D. index of lens material relative to surrounding medium

• **index of lens material relative to surrounding medium** = the lens maker's equation uses the refractive index of the lens glass relative to the surrounding medium; 1/f = (n−1)(1/R1 − 1/R2), where n is this relative index. • **Relative n matters** — a lens in air behaves differently from the same lens in water because the relative refractive index n changes; a converging lens in air can become diverging if submerged in a medium of higher index. • 💡 Wrong-option analysis: ratio of lens thickness to radius only: lens thickness and radius relate to geometry (sagitta approximation), not directly to refractive index in the lens maker's context; ratio of focal length to aperture: focal length to aperture ratio is the f-number (f/D), which describes camera optics but is not the refractive index; unit of power in diopters: diopters is the unit of lens power (1/f in metres) — refractive index is dimensionless and expressed as a pure number.

Correct Answer: D. depends on wavelength (color)

• **depends on wavelength (color)** = the refractive index n of a material varies with wavelength (Cauchy's equation: n = A + B/λ²); different colours bend by different amounts, spreading white light into a spectrum. • **n_violet > n_red** — violet light (shorter wavelength) has a higher n and bends more than red light (longer wavelength); this differential bending is dispersion. • 💡 Wrong-option analysis: depends only on prism mass: refractive index is an optical property of the material, independent of the mass or size of the prism; depends only on temperature and never on color: temperature does slightly affect n, but the primary cause of dispersion is wavelength dependence — colour is the key variable; is always equal to 1: n = 1 only for vacuum; glass has n between 1.5 and 1.9 depending on type, so dispersion cannot occur if n were always 1.

Correct Answer: A. Violet

• **Violet** = in ordinary glass, violet light (wavelength ~400 nm) has the highest refractive index among visible colours because n increases as wavelength decreases (normal dispersion). • **VIBGYOR order** — the sequence of n from highest to lowest follows violet > indigo > blue > green > yellow > orange > red; violet bends most in a prism and appears at the bottom of the spectrum. • 💡 Wrong-option analysis: Yellow: yellow (wavelength ~580 nm) falls in the middle of the visible spectrum; its n is moderate — not the highest; Green: green (~530 nm) is between yellow and blue in wavelength; its n is higher than red/yellow but lower than blue/violet; Red: red light (wavelength ~700 nm) has the longest visible wavelength and correspondingly the lowest refractive index in normal dispersion.

Correct Answer: A. n21 = v1/v2

• **n21 = v1/v2** = the relative refractive index of medium 2 with respect to medium 1 equals the ratio of light speeds: n21 = v1/v2; it also equals n2/n1 (ratio of absolute indices). • **Equivalent forms** — n21 = v1/v2 = n2/n1; if v1 > v2 then n21 > 1 meaning medium 2 is denser, and light slows down going from 1 to 2. • 💡 Wrong-option analysis: n21 = n1 + n2: adding absolute refractive indices has no physical meaning — n21 is a ratio, not a sum; n21 = v2/v1: this is the inverse; v2/v1 = n1/n2 = n12 (index of medium 1 w.r.t. medium 2), not n21; n21 = n1/n2: n1/n2 = n12 (index of medium 1 w.r.t. medium 2) — the numerator and denominator are swapped.

Correct Answer: A. decreases

• **decreases** = from v = c/n, a higher refractive index n directly gives a lower speed v; light always slows down when entering an optically denser medium. • **Cause of bending** — it is this decrease in speed that causes the wavefront to tilt and the ray to bend towards the normal at the boundary. • 💡 Wrong-option analysis: increases: speed increases when going to a lower n medium (rarer), not higher; this would be the case for light leaving glass into air; becomes zero always: speed is zero only at absolute zero for certain exotic condensates — in normal glass or water light still travels at about 0.6–0.75c; becomes infinite: infinite speed would violate special relativity; in any physical medium v ≤ c.

Correct Answer: C. decreases

• **decreases** = in normal dispersion (the usual case for glass in the visible range), shorter wavelength light has higher n; as λ decreases, n increases. • **Cauchy relation** — n ≈ A + B/λ² shows n rising as λ falls; this means violet (short λ) bends more than red (long λ) in a prism. • 💡 Wrong-option analysis: is unrelated to refractive index: dispersion is precisely the dependence of n on wavelength — they are directly related; increases: if n increased with wavelength, red would bend more than violet (anomalous dispersion in special media), not normal dispersion of glass; becomes zero: wavelength becoming zero is not a physical scenario in normal optics — and even approaching zero would just mean very high n, not a separate case.