Refraction — Set 2

Correct Answer: A. total internal reflection in layers of air

• **total internal reflection in layers of air** = on a hot road, air near the ground is hotter and less dense (lower n) than air above; light traveling downward is progressively refracted and eventually undergoes total internal reflection, making the road look like a water surface. • **Temperature gradient** — the refractive index gradient in hot air near the ground acts like a concave 'lens' that curves light rays upward; the sky reflection is what appears as the illusory water pool. • 💡 Wrong-option analysis: scattering only: scattering (Rayleigh type) explains the blue sky and red sunsets but does not create the inverted sky image seen in a mirage; diffraction only: diffraction involves bending around obstacles or through slits — it cannot create an inverted sky image on a hot road; polarization only: polarization describes the orientation of the electric field in a light wave and has no mechanism for producing mirage images.

Correct Answer: B. refraction through moving air layers

• **refraction through moving air layers** = starlight passes through atmospheric layers of constantly changing temperature, density, and refractive index; turbulent air shifts the apparent position and brightness of the star rapidly, causing twinkling (scintillation). • **Stars vs planets** — stars are point sources at huge distances, so even tiny refractive shifts randomise their brightness; planets appear as extended discs, so the averaging effect suppresses twinkling — planets do not twinkle noticeably. • 💡 Wrong-option analysis: absorption in space: absorption in interstellar space is extremely small and uniform — it cannot cause rapid brightness fluctuations on time scales of milliseconds; diffraction by the eye: the eye's aperture is far too large to produce diffraction effects that cause twinkling — diffraction affects colour fringing, not random brightness variation; reflection from clouds: reflection from clouds would block or redirect starlight uniformly, not cause the rapid intensity variations that constitute twinkling.

Correct Answer: C. refraction, dispersion, and internal reflection

• **refraction, dispersion, and internal reflection** = sunlight enters a raindrop and refracts; dispersion splits it into colours because n varies with wavelength; one internal reflection occurs inside the drop; the light refracts again on exit, producing the arc of colours. • **Primary rainbow angles** — red exits at ~42° and violet at ~40° from the anti-solar point because violet has a higher n and bends more; a secondary rainbow (two internal reflections) appears at ~51°. • 💡 Wrong-option analysis: only dispersion without refraction: dispersion is caused by different amounts of refraction for different wavelengths — dispersion cannot exist without refraction; only diffraction: diffraction by water droplets produces a corona around the sun or moon (much smaller ring), not the large rainbow arc; only reflection: pure reflection without refraction and dispersion would send white light back without separating colours — no rainbow.

Correct Answer: D. goes straight without deviation

• **goes straight without deviation** = at normal incidence i = 0°; by Snell's law n1 sin 0° = n2 sin r, so sin r = 0 and r = 0°; the ray continues in the same direction with no bending. • **Speed and wavelength still change** — although the direction is unchanged, the speed and wavelength of light change at the boundary; only direction is unaffected. • 💡 Wrong-option analysis: bends away from the normal: bending away occurs when going from denser to rarer medium at oblique incidence — not at normal incidence; travels along the surface: traveling along the surface corresponds to r = 90°, which is the definition of the critical angle, not normal incidence; bends towards the normal: bending towards the normal occurs at oblique incidence going into a denser medium, not at i = 0°.

Correct Answer: B. 2.0×10^8 m/s

• **2.0×10^8 m/s** = use v = c/n; with c = 3.0×10^8 m/s and n = 1.5, v = 3.0×10^8 / 1.5 = 2.0×10^8 m/s. • **n = 1.5** — the medium slows light to two-thirds of its vacuum speed; this is roughly the speed in common glass. • 💡 Wrong-option analysis: 1.5×10^8 m/s: this would require n = c / v = 3.0/1.5 = 2.0, not 1.5 — it corresponds to a denser medium; 4.5×10^8 m/s: this exceeds c, which is impossible for light in any medium; 3.0×10^8 m/s: that is the speed in vacuum (n = 1), not in a medium with n = 1.5.

Correct Answer: C. 375 nm

• **375 nm** = wavelength in a medium is λ_medium = λ_air / n; with λ_air = 600 nm and n = 1.6, λ_glass = 600 / 1.6 = 375 nm. • **Frequency unchanged** — the frequency of light does not change on entering glass; since v = fλ and v decreases, λ must decrease by the same factor n, giving a shorter wavelength inside the glass. • 💡 Wrong-option analysis: 600 nm: 600 nm is the wavelength in air; in glass the speed (and hence wavelength) decreases — it cannot remain 600 nm; 1.6 nm: 1.6 nm is simply the value of the refractive index in nm units, not a wavelength — this has no physical meaning; 960 nm: 960 = 600 × 1.6, which would require the wavelength to increase on entering glass — in reality it decreases.

Correct Answer: C. Higher refractive index generally means optically denser medium

• **Higher refractive index generally means optically denser medium** = 'optical density' is a qualitative term used to compare how strongly two media slow down light; the medium with the higher refractive index is called optically denser. • **Not mass density** — optical density is based on refractive index, not physical mass density; water (mass density ~1000 kg/m³) is optically denser than turpentine oil even though turpentine is lighter. • 💡 Wrong-option analysis: Optical density means physical mass density only: optical density and mass density are different properties — a medium can be optically dense but physically light (e.g. turpentine); Optical density depends only on color of the medium: refractive index (and hence optical density) depends on the wavelength of light and the material, not merely on the colour of the medium; Optical density is always the same for all materials: different materials slow light by different amounts, so their optical densities differ.

Correct Answer: D. parallel to the incident ray

• **parallel to the incident ray** = refraction at the first face bends the ray; refraction at the second parallel face bends it back by exactly the same angle; the net angular deviation is zero, so the emergent ray is parallel to the incident ray. • **Lateral displacement** — although the emergent ray is parallel, it is shifted sideways (laterally displaced) by an amount that increases with slab thickness and angle of incidence. • 💡 Wrong-option analysis: always perpendicular to the slab: the emergent ray is perpendicular only if the incident ray is perpendicular (normal incidence); for oblique incidence the ray is not perpendicular; always deviated by 90 degrees: 90° deviation would require a very specific geometry — it is not a general result for a parallel slab; always reflected back: total internal reflection back into the slab requires i > critical angle at the glass-air boundary; for normal glass (n = 1.5, critical angle ≈ 42°) light mostly transmits.

Correct Answer: C. increasing slab thickness

• **increasing slab thickness** = the formula for lateral displacement is d = t sin(i − r) / cos r; for fixed i and n, the displacement grows linearly with the thickness t of the slab. • **d = t sin(i − r) / cos r** — at i = 0, d = 0 (no displacement); as t increases the ray travels a longer oblique path inside the slab, producing greater lateral shift on exit. • 💡 Wrong-option analysis: decreasing refractive index to 1: as n → 1, refraction angle r → incidence angle i, so (i − r) → 0 and displacement → 0 — decreasing n reduces displacement; decreasing angle of incidence to zero: at i = 0 the ray passes straight through and d = 0; displacement increases with i, not decreases; decreasing slab thickness: decreasing thickness reduces the lateral path length inside the slab and hence reduces displacement.

Correct Answer: A. angle of incidence equals angle of emergence

• **angle of incidence equals angle of emergence** = at minimum deviation the ray path inside the prism is symmetric; by symmetry the angle of incidence at the first face equals the angle of emergence at the second face (i1 = i2). • **r1 = r2 = A/2** — since the path is symmetric, the internal refraction angles at both faces are equal and each equals half the prism angle A; this condition is used to derive the minimum deviation formula. • 💡 Wrong-option analysis: i = 0 always: i = 0 would mean normal incidence, causing no refraction and no deviation — not minimum deviation; r1 = 0 always: r1 = 0 would require the ray to travel along the bisector of the prism without bending at the first face — this is not the minimum deviation condition; Dm is maximum: Dm is by definition a minimum (the smallest deviation achievable); calling it maximum contradicts its definition.