Total Internal Reflection — Revision Notes

⚡ 30-Second Revision

Conditions for TIR:

1. Light travels from denser to rarer medium ($n_1 > n_2$). 2. Angle of incidence $i > \theta_c$.

Critical Angle Formula: — $sin \theta_c = \frac{n_{rarer}}{n_{denser}}$
For air as rarer medium: — $sin \theta_c = \frac{1}{n_{denser}}$
At critical angle: — Angle of refraction $r = 90^circ$.
Key Applications: — Optical fibers, diamonds, mirages, reflecting prisms.

2-Minute Revision

Total Internal Reflection (TIR) is a phenomenon where light, instead of refracting, is completely reflected back into its original medium. This occurs under two strict conditions: first, light must travel from an optically denser medium (higher refractive index) to an optically rarer medium (lower refractive index).

Second, the angle of incidence in the denser medium must be greater than the critical angle ($heta_c$). The critical angle is defined as the angle of incidence for which the angle of refraction is exactly $90^circ$, meaning the refracted ray grazes the interface.

Its value is calculated using $sin \theta_c = n_{rarer}/n_{denser}$. If the rarer medium is air, $sin \theta_c = 1/n_{denser}$. TIR is 100% efficient, making it superior to metallic mirrors for certain applications.

Key examples include optical fibers for telecommunication, the sparkling of diamonds, the formation of mirages, and the use of reflecting prisms in binoculars and periscopes. Remember, TIR cannot occur if light travels from a rarer to a denser medium.

5-Minute Revision

Total Internal Reflection (TIR) is a crucial concept in optics, describing the complete reflection of a light ray back into the denser medium from which it originated. This happens when two specific conditions are met:

1
Direction of Travel: — Light must be propagating from an optically denser medium (higher refractive index, $n_1$) to an optically rarer medium (lower refractive index, $n_2$). For example, from water to air, or glass to air.
2
Angle of Incidence: — The angle of incidence ($i$) in the denser medium must be greater than the critical angle ($heta_c$).

The **critical angle ($heta_c$)** is a unique angle of incidence for a given pair of media. It is the angle at which the refracted ray in the rarer medium makes an angle of $90^circ$ with the normal, effectively grazing the interface.

Using Snell's Law ($n_1 sin i = n_2 sin r$), we can derive the formula for the critical angle: when $i = \theta_c$, $r = 90^circ$, so $n_1 sin \theta_c = n_2 sin 90^circ = n_2$. Thus, $sin \theta_c = n_2/n_1$.

If the rarer medium is air ($n_2 approx 1$), the formula simplifies to $sin \theta_c = 1/n_1$.

Worked Example: Calculate the critical angle for a glass-water interface, given $n_{glass} = 1.5$ and $n_{water} = 1.33$.

Here, glass is denser ($n_1 = 1.5$) and water is rarer ($n_2 = 1.33$).
$sin \theta_c = n_{water}/n_{glass} = 1.33/1.5 approx 0.8867$.
$heta_c = arcsin(0.8867) approx 62.4^circ$.

Applications of TIR are widespread:

Optical Fibers: — Light signals are guided through a core (denser) by repeated TIR at the core-cladding (rarer) interface, enabling high-speed data transmission.
Diamonds: — Their high refractive index leads to a small critical angle, causing multiple TIRs within the facets, resulting in their characteristic sparkle.
Mirages: — Formed in deserts due to TIR of light from cooler (denser) air layers to hotter (rarer) air layers near the ground.
Reflecting Prisms: — Used in binoculars and periscopes to deviate light by $90^circ$ or $180^circ$ with 100% efficiency, superior to mirrors.

Remember that TIR is distinct from regular reflection; it's an extreme case of refraction and is ideally 100% efficient. Always check the direction of light travel before applying TIR principles.

Prelims Revision Notes

Total Internal Reflection (TIR) is a critical phenomenon in optics for NEET. It occurs when light travels from an optically denser medium ($n_1$) to an optically rarer medium ($n_2$) and the angle of incidence ($i$) exceeds the critical angle ($heta_c$).

Key Formulas and Concepts:

Refractive Index ($n$): — $n = c/v$. Denser medium has higher $n$, rarer medium has lower $n$.
Snell's Law: — $n_1 sin i = n_2 sin r$.
Critical Angle ($ heta_c$): — The angle of incidence in the denser medium for which the angle of refraction in the rarer medium is $90^circ$.
Formula for $ heta_c$: — $sin \theta_c = n_{rarer}/n_{denser}$.

* If the rarer medium is air ($n_{air} approx 1$), then $sin \theta_c = 1/n_{denser}$.

Conditions for TIR:

1. Light must travel from denser to rarer medium ($n_1 > n_2$). 2. Angle of incidence $i > \theta_c$.

Important Points to Remember:

If $i < \theta_c$: Refraction occurs, light passes into the rarer medium.
If $i = \theta_c$: Refracted ray grazes the interface ($r = 90^circ$).
If $i > \theta_c$: Total Internal Reflection occurs, light reflects back into the denser medium.
TIR is 100% efficient, unlike ordinary reflection from mirrors.
TIR cannot occur if light travels from a rarer medium to a denser medium, as the angle of refraction can never reach $90^circ$.
The critical angle depends on the pair of media and slightly on the wavelength of light (due to dispersion).

Applications to Memorize:

Optical Fibers: — Core (denser) and cladding (rarer) ensure light transmission via repeated TIR.
Sparkling of Diamonds: — High $n$ leads to small $heta_c$, causing multiple TIRs.
Mirages: — Light from cooler (denser) air layers undergoes TIR as it approaches hotter (rarer) ground layers.
Reflecting Prisms: — Used in periscopes, binoculars to turn light by $90^circ$ or $180^circ$ using TIR, offering better reflection than mirrors.
Endoscopes: — Medical instruments using optical fibers for internal viewing.

Practice numerical problems involving critical angle calculations and conceptual questions distinguishing TIR from other optical phenomena.

Vyyuha Quick Recall

Denser-Rarer, Angle Greater, Ninety-Degree Refractor! (Denser-Rarer: Light from denser to rarer. Angle Greater: Angle of incidence greater than critical angle. Ninety-Degree Refractor: At critical angle, refraction is 90 degrees.)