Vardaan Learning Institute

Absolute refractive index $n_m = c/v_m$.

Frequency remains constant as it depends on the source. Speed decreases ($v = c/n$) and wavelength decreases ($\lambda' = \lambda/n$).

Refractive index of glass w.r.t water $_w n_g = n_g / n_w = 1.50 / 1.33$.

Since speed of light in vacuum ($c$) is maximum, $n = c/v$ is always $>1$.

$n = c/v = (3 \times 10^8) / (2 \times 10^8) = 1.5$.

When light travels from denser to rarer medium, its speed increases, bending it away from the normal.

Higher refractive index means higher optical density. Even though kerosene floats on water (lower mass density), it is optically denser.

It is a ratio of two similar physical quantities (speeds).

Violet has the shortest wavelength and maximum refractive index, so it bends (deviates) the most.

This is Snell's Law.

Refractive index $n = c/v$. High $n$ means very low $v$.

Assertion is False: Air to glass is Rare to Denser, so it bends towards the normal. Wait, the option says "bends towards the normal". Ah, check statement carefully. Wait, Reason says "Light travels faster in glass". That is FALSE. Light travels slower in glass. So R is False. Correct option: (c) A is True, R is False. (Self-Correction: Text says A: Air to glass bends towards normal - True. R: Light faster in glass - False. Result: C).

Units cancel out in the ratio.

Formula: $n_g = c / v_g$
$1.50 = (3 \times 10^8) / v_g$
$v_g = (3 \times 10^8) / 1.50 = 2 \times 10^8$ m/s.

$n = c/v$, so velocity is inversely proportional to refractive index ($v \propto 1/n$).
Since $n_B (1.33) < n_A (1.5)$, speed of light is greater in Medium B.

$n = c/v = (3 \times 10^8) / (2.25 \times 10^8) = 300 / 225 = 4/3 = 1.33$.

First Law: The incident ray, the refracted ray and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.
Second Law (Snell's Law): The ratio of sine of angle of incidence to the sine of angle of refraction is a constant ($n$) for the light of a given color and for the given pair of media.

Rays of light coming from the part of the pencil inside water travel from water (denser) to air (rarer). They bend away from the normal. When produced backwards, they appear to meet at a point higher than the actual position, causing the pencil to look bent at the interface.

We need Refractive Index of Turpentine w.r.t Alcohol $_a n_t$.
$_a n_t = n_{turpentine} / n_{alcohol} = 1.47 / 1.36 \approx 1.08$.

This is due to refraction. Light rays from the coin travel from water to air and bend away from the normal. To an observer, these rays appear to come from a point slightly above the actual bottom, creating a virtual image of the coin at a lesser depth (Apparent Depth).

Given $_a n_w = 4/3$ and $_a n_g = 3/2$.
We need $_w n_g = n_g / n_w = (3/2) / (4/3) = (3/2) \times (3/4) = 9/8 = 1.125$.

Optical Density: The ability of a medium to refract light. Higher optical density means slower speed of light.
Difference: Mass density is mass per unit volume. Optical density is related to speed of light.
Example: Kerosene is optically denser than water ($n=1.44 > 1.33$) but has lower mass density (it floats on water).

Snell's Law: $n_{21} = \sin i / \sin r$.
$n_{21} = \sin 45 / \sin 30 = 0.707 / 0.5 = 1.414$.

(a) Absolute refractive index is the ratio of speed of light in vacuum to the speed of light in the medium. $n_m = c/v_m$.
(b) Given $v = 0.6c$.
$n = c/v = c / (0.6c) = 1/0.6 = 10/6 = 1.67$.
(c) Light bends because its speed changes when entering a different medium. One part of the wavefront changes speed before the other, causing the direction of propagation to shift.

(i) The perpendicular distance between the incident ray produced forward and the emergent ray is called lateral displacement.
(ii) Factors: Thickness of slab, Angle of incidence, Refractive index of material.
(iii) If refractive index increases, lateral displacement increases (light bends more).

(a) $_a n_w = n_w/n_a$, $_w n_g = n_g/n_w$, $_g n_a = n_a/n_g$.
Product $= (n_w/n_a) \times (n_g/n_w) \times (n_a/n_g) = 1$. (Everything cancels out).
(b) Critical angle definition: The angle of incidence in the denser medium for which the angle of refraction in the rarer medium becomes $90^\circ$. Relationship: $\sin C = 1/n$.

Calculations ($v=c/n$):
Water: $3 \times 10^8 / 1.33 \approx 2.25 \times 10^8$ m/s.
Glass: $3 \times 10^8 / 1.50 = 2.00 \times 10^8$ m/s.
Diamond: $3 \times 10^8 / 2.42 \approx 1.24 \times 10^8$ m/s.
Increasing Optical Density: Water < Glass < Diamond.

(a) Stars are point sources; atmospheric turbulence constantly changes the path of light (refractive index fluctuates), causing 'twinkling'. Planets are extended sources; shifts in light path from different points average out to zero net change.
(b) Atmospheric refraction bends sunlight from below the horizon towards the observer. Air near earth is denser than higher layers. Light travels from rarer to denser, bending towards normal (earth surface), making the sun visible about 2 mins before actual sunrise.

(i) $n = \sin i / \sin r \implies 1.5 = \sin 60 / \sin r$.
$\sin r = \sin 60 / 1.5 = 0.866 / 1.5 = 0.577$.
$r = \sin^{-1}(0.577) \approx 35.3^\circ$.
(ii) Emergent ray comes back to air. Snell's law at second interface: $1/n = \sin r / \sin e$.
$n \sin r = \sin e$. Since $n = \sin i / \sin r$, we get $\sin i = \sin e \implies \angle i = \angle e$. Hence emergent ray is parallel.

(i) Max Speed: Medium A (Lowest RI 1.3).
(ii) Min Speed: Medium C (Highest RI 2.0).
(iii) A to B (Rare to Denser): Bends Towards Normal.
(iv) C to B (Denser to Rare): Bends Away from Normal.