Refraction — Set 1

Correct Answer: B. Bending of light due to change in speed in a new medium

• **Refraction** = bending of light that occurs at the boundary of two transparent media because the speed of light changes as it enters the new medium. • **Speed change** — in a denser medium light slows down, causing the ray to bend towards the normal; in a rarer medium it speeds up and bends away. • 💡 Wrong-option analysis: Splitting of white light into colors: that is dispersion, a consequence of different wavelengths having different refractive indices, not the definition of refraction; Reflection of light from a surface: reflection sends light back into the same medium — refraction passes light into the new medium; Blocking of light by an object: that describes opacity or shadow formation, not refraction.

Correct Answer: B. n1 sin i = n2 sin r

• **n1 sin i = n2 sin r** = Snell's law states that the product of refractive index and sine of the angle (measured from the normal) is conserved across the boundary. • **Constant product** — n1 sin i = n2 sin r means that if n2 > n1 (denser medium), sin r < sin i, so the refracted ray bends towards the normal. • 💡 Wrong-option analysis: n1 cos i = n2 cos r: uses cosines instead of sines — this has no physical basis in standard refraction; n1 + n2 = sin i + sin r: mixing indices and angles by addition is dimensionally inconsistent; n1/n2 = sin r / sin i: this is an inverted form — Snell's law gives n1/n2 = sin r / sin i only when the ratio is taken the wrong way round.

Correct Answer: C. n = c/v

• **n = c/v** = the absolute refractive index of a medium equals the speed of light in vacuum (c) divided by the speed of light in that medium (v). • **n ≥ 1** — since light slows in any material medium (v ≤ c), the refractive index is always greater than or equal to 1; for vacuum n = 1 exactly. • 💡 Wrong-option analysis: n = v/c: this inverts the ratio and would give n ≤ 1, making vacuum the densest medium — incorrect; n = c - v: subtracting speeds gives units of m/s, but refractive index is dimensionless; n = c + v: adding speeds also gives units of m/s and has no physical meaning for refractive index.

Correct Answer: B. Towards the normal

• **Towards the normal** = glass is optically denser than air (n_glass > n_air), so light slows down on entering glass and the refracted ray bends towards the normal. • **Snell's law** — n_air sin i = n_glass sin r; since n_glass > n_air, sin r < sin i, confirming r < i and the bend is towards the normal. • 💡 Wrong-option analysis: No bending at all: bending only disappears at normal incidence (i = 0°); for any oblique ray there is bending; Away from the normal: that happens when going from denser to rarer medium (e.g. glass to air), not air to glass; Bends along the surface: the refracted ray travels through the glass, not along its surface — 'along the surface' corresponds to the critical angle condition.

Correct Answer: A. Frequency

• **Frequency** = the frequency of light is set by the source and cannot change at a boundary; it remains constant during refraction. • **λ = v/f** — since v changes and f stays constant, wavelength λ = v/f changes proportionally to the speed, while frequency does not. • 💡 Wrong-option analysis: Wavelength: wavelength changes because speed changes (λ = v/f); Wavelength = speed/frequency, so shorter wavelength in denser medium; Speed: speed is precisely what changes at the boundary, causing the bending; Direction always stays same: direction changes (that is what refraction means) unless the ray hits normally.

Correct Answer: A. It decreases

• **It decreases** = in a denser medium speed decreases while frequency stays constant; since λ = v/f, a smaller v gives a smaller λ. • **λ_medium = λ_air / n** — the wavelength in a medium of refractive index n is shorter than in air by the factor n; e.g. for n = 1.5, wavelength reduces to two-thirds of its air value. • 💡 Wrong-option analysis: It becomes zero: wavelength becoming zero would require speed = 0, which never happens for light in a physical medium; It increases: wavelength increases when entering a rarer medium (lower n), not a denser one; It becomes infinite: infinite wavelength would require infinite speed, which violates special relativity.

Correct Answer: B. n = c/v

• **n = c/v** = absolute refractive index is defined as the ratio of the speed of light in vacuum (c) to the speed in the medium (v). • **Dimensionless** — c and v both have the same units (m/s), so their ratio n is a pure number with no units; it characterises the optical density of the medium. • 💡 Wrong-option analysis: n = f/λ: f/λ equals v (speed = frequency × wavelength), not a dimensionless ratio; this gives m/s, not refractive index; n = 1/(c+v): dividing by (c+v) gives units of s/m, which is dimensionally wrong; n = v/c: this is the reciprocal of the correct definition and would give values ≤ 1 for all real media.

Correct Answer: C. less than real depth

• **less than real depth** = when viewed from the rarer medium (air), refraction bends rays away from the normal; the refracted rays appear to diverge from a point shallower than the actual object, giving apparent depth = real depth / n. • **apparent depth = real depth / n** — for water (n ≈ 1.33), a 1.33 m deep pool appears only 1.0 m deep; the bottom looks raised. • 💡 Wrong-option analysis: infinite: infinite apparent depth would require the emergent rays to be parallel, which happens only when the object is at the critical-angle boundary, not for normal viewing; greater than real depth: apparent depth is greater than real depth when viewed from inside the denser medium looking into a rarer one; equal to real depth always: equal depth only applies when both observer and object are in the same medium.

Correct Answer: D. denser medium to rarer medium

• **denser medium to rarer medium** = critical angle is the specific angle of incidence (inside the denser medium) at which the refracted ray just grazes the boundary, making an angle of refraction of 90°. • **sin c = n_rarer / n_denser** — beyond this angle, total internal reflection occurs; the condition is only physically possible when going from denser to rarer, since refraction into the denser medium always produces r < 90°. • 💡 Wrong-option analysis: air to vacuum only: air to vacuum is rarer to rarer (both n ≈ 1), so no critical angle exists; any medium at any direction: going from rarer to denser always bends the ray towards the normal and refraction always occurs — no critical angle; rarer medium to denser medium: when entering a denser medium, the refracted angle is always less than 90°, so there is no critical angle condition.

Correct Answer: B. angle of incidence is greater than critical angle

• **angle of incidence is greater than critical angle** = when i > critical angle in the denser medium, Snell's law would require sin r > 1, which is impossible; instead, the light is completely reflected back into the denser medium. • **Two conditions** — (1) light must travel from denser to rarer medium and (2) the angle of incidence must exceed the critical angle; both conditions must hold simultaneously. • 💡 Wrong-option analysis: angle of incidence is zero: at i = 0 the light goes straight through normally with no TIR; angle of refraction is smaller than incidence: this is always true when going from denser to rarer medium with any i below the critical angle — normal refraction, not TIR; media have equal refractive index: equal indices means no bending at all, not total internal reflection.