Refraction of Light — Revision Notes

⚡ 30-Second Revision

Refraction: — Bending of light as it passes from one transparent medium to another due to change in speed.
Refractive Index ($n$): — $n = c/v$. Ratio of speed of light in vacuum ($c$) to speed in medium ($v$).
Snell's Law: — $n_1 sin \theta_1 = n_2 sin \theta_2$.
Rarer to Denser: — Light bends towards normal ($heta_2 < \theta_1$).
Denser to Rarer: — Light bends away from normal ($heta_2 > \theta_1$).
Normal Incidence: — No bending ($heta_1 = \theta_2 = 0^circ$).
Frequency: — Remains constant during refraction.
Wavelength: — Changes, $lambda' = lambda/n$.
Total Internal Reflection (TIR): — Occurs when light goes from denser to rarer medium and $heta_1 > \theta_c$.
Critical Angle ($ heta_c$): — $sin \theta_c = n_{rarer}/n_{denser}$.
Apparent Depth: — $d_{apparent} = d_{real}/n_{medium}$ (viewed from air into medium).
Lateral Shift: — For a glass slab, $x = t sin(\theta_1 - \theta_2) / cos \theta_2$.

2-Minute Revision

Refraction is the phenomenon of light changing direction when it passes from one transparent medium to another, primarily due to a change in its speed. The extent of bending is quantified by the refractive index ($n$), defined as the ratio of the speed of light in vacuum to its speed in the medium ($n=c/v$).

Snell's Law, $n_1 sin \theta_1 = n_2 sin \theta_2$, is the governing principle, relating the angles of incidence and refraction to the refractive indices of the two media. Light bends towards the normal when entering a denser medium and away from the normal when entering a rarer medium.

Crucially, the frequency of light remains constant during refraction, while its speed and wavelength change. A significant consequence is Total Internal Reflection (TIR), which occurs when light travels from a denser to a rarer medium at an angle greater than the critical angle ($heta_c$), where $sin \theta_c = n_{rarer}/n_{denser}$.

Refraction also explains apparent depth, where submerged objects appear shallower, given by $d_{apparent} = d_{real}/n$. These concepts are fundamental for understanding lenses, prisms, and various optical phenomena.

5-Minute Revision

Refraction is the directional change of light as it crosses the boundary between two transparent media, a phenomenon driven by the alteration of light's speed. Each medium possesses a unique optical density, quantified by its refractive index ($n = c/v$), where $c$ is the speed of light in vacuum and $v$ is its speed in the medium.

A higher refractive index implies a slower speed of light. The core law governing refraction is Snell's Law: $n_1 sin \theta_1 = n_2 sin \theta_2$. Here, $n_1$ and $n_2$ are the refractive indices of the first and second media, respectively, while $heta_1$ and $heta_2$ are the angles of incidence and refraction, measured with respect to the normal.

When light moves from a rarer to a denser medium ($n_2 > n_1$), it bends towards the normal ($heta_2 < \theta_1$). Conversely, from denser to rarer ($n_2 < n_1$), it bends away from the normal ($heta_2 > \theta_1$).

If light is incident normally ($heta_1 = 0^circ$), it passes undeviated, with $heta_2 = 0^circ$.

An important point for NEET is that while the speed and wavelength of light change during refraction ($v = flambda$), its frequency ($f$) remains constant, as it's determined by the source. The wavelength changes as $lambda' = lambda/n$.

Total Internal Reflection (TIR) is a critical concept. It occurs when light travels from a denser medium to a rarer medium, and the angle of incidence exceeds the critical angle ($heta_c$). The critical angle is defined by $sin \theta_c = n_{rarer}/n_{denser}$. If $heta_1 > \theta_c$, all light is reflected back into the denser medium, making TIR a highly efficient reflection process. Applications include optical fibers and prism binoculars.

Another key application is apparent depth. An object submerged in a denser medium (like water) appears shallower when viewed from a rarer medium (like air) due to refraction. The relationship is $d_{apparent} = d_{real}/n$, where $n$ is the refractive index of the denser medium with respect to the rarer medium.

For example, a coin at $10,\text{cm}$ depth in water ($n=4/3$) would appear at $10 / (4/3) = 7.5,\text{cm}$ depth. Mastering these formulas and their conceptual underpinnings is vital for NEET success.

Prelims Revision Notes

Refraction of Light: NEET Quick Recall

1. Definition & Cause:

Refraction: — Bending of light as it passes from one transparent medium to another.
Cause: — Change in the speed of light ($v$) as it enters a new medium. Frequency ($f$) remains constant, but wavelength ($lambda$) changes ($v = flambda$).

2. Refractive Index ($n$):

Absolute Refractive Index: — $n = c/v$, where $c$ is speed of light in vacuum, $v$ is speed in medium.
Relative Refractive Index: — $n_{21} = n_2/n_1 = v_1/v_2$.
$n ge 1$ (for vacuum, $n=1$; for air, $n approx 1.0003$).
Higher $n implies$ optically denser medium, slower light.

3. Snell's Law:

Statement: — $n_1 sin \theta_1 = n_2 sin \theta_2$.
$heta_1$: Angle of incidence (ray to normal in medium 1).
$heta_2$: Angle of refraction (ray to normal in medium 2).
Bending Rules:

* Rarer to Denser ($n_1 < n_2$): Bends towards normal ($heta_2 < \theta_1$). * Denser to Rarer ($n_1 > n_2$): Bends away from normal ($heta_2 > \theta_1$). * Normal Incidence ($heta_1 = 0^circ$): No bending ($heta_2 = 0^circ$).

4. Total Internal Reflection (TIR):

Conditions:

1. Light travels from a denser medium to a rarer medium. 2. Angle of incidence ($heta_1$) in the denser medium must be **greater than the critical angle ($heta_c$)**.

Critical Angle ($ heta_c$): — Angle of incidence for which $heta_2 = 90^circ$.

* Formula: $sin \theta_c = n_{rarer}/n_{denser}$.

Applications: — Optical fibers, sparkling of diamond, mirages, prism binoculars.

5. Apparent Depth:

Object in denser medium viewed from rarer medium appears shallower.
Formula (viewing from air into a medium): $n_{medium} = d_{real}/d_{apparent}$.
Shift: $Delta d = d_{real} - d_{apparent} = d_{real}(1 - 1/n)$.

6. Lateral Shift (for a glass slab):

When light passes through a parallel-sided glass slab, it emerges parallel to the incident ray but laterally shifted.
Lateral shift $x = t sin(\theta_1 - \theta_2) / cos \theta_2$, where $t$ is slab thickness.

7. Dispersion:

Refractive index varies with wavelength ($n_{violet} > n_{red}$). This causes white light to split into colors (e.g., prism, rainbow).

Key Points to Remember:

Always measure angles with respect to the normal.
Frequency is invariant during refraction.
TIR is 100% efficient reflection.
Draw ray diagrams for clarity in complex problems.

Vyyuha Quick Recall

To remember Snell's Law: Nice Sinners Take Nice Sinners Together. (N1 Sin Theta1 = N2 Sin Theta2). Or, for the bending direction: Rarer to Denser, Towards Normal (RDTN). Denser to Rarer, Away from Normal (DRAN).