A light ray travelling in glass medium is incident on glass-air interface at an angle of incidence t

Q: Why isn't transmission 100% at $\theta = 0^\circ$?

Even when light hits a boundary perfectly straight, the change in refractive index causes a small portion of the wave to bounce back. This is governed by Fresnel's equations, which show that $R = \left(\frac{n_1 - n_2}{n_1 + n_2}\right)^2$ at normal incidence.

Q: What exactly happens at the critical angle?

At the critical angle, the refracted ray grazes the surface of the boundary (angle of refraction is $90^\circ$). The transmitted intensity drops to exactly zero, and 100% of the light energy is reflected back into the denser medium.

Q: Why does graph (b) look wrong?

Graph (b) suggests that transmission remains perfectly at 100% and reflection at 0% until the critical angle is reached, at which point they instantly snap to 0% and 100%. In reality, the transition is smooth and continuous as the angle increases.

Q: Does the intensity of the reflected ray always increase with the angle of incidence?

For light moving from a denser to a rarer medium, the overall reflected intensity generally increases with the angle of incidence, culminating in 100% reflection at and beyond the critical angle.

Q: Why do we care about Total Internal Reflection?

TIR is the fundamental principle behind optical fibers, which carry the internet across oceans! It's also why diamonds sparkle so brilliantly and how mirages form on hot days.

Question

A light ray travelling in glass medium is incident on glass-air interface at an angle of incidence $	heta$. The reflected ($R$) and transmitted ($T$) intensities, both as function of $	heta$, are plotted. The correct sketch is

Sigma Percentile · Accepted Answer

### The Boundary of Two Worlds

Imagine a light ray travelling from a denser medium, like glass, into a rarer medium, like air.

When it hits the boundary, it doesn't just pass through seamlessly.

A part of the light energy is reflected back into the glass, and the remaining portion is transmitted into the air.

This fundamental behavior is governed by the laws of reflection and refraction, and it sets the stage for a fascinating interplay between the reflected intensity $R$ and the transmitted intensity $T$.

### The Myth of Perfect Transmission

Let's think about what happens when the light hits the surface exactly straight on, at an angle of incidence $	heta = 0^\circ$.

Is all the light transmitted? No!

Even at normal incidence, a small fraction of light is always reflected due to the difference in refractive indices of the two media.

Mathematically, the reflection coefficient at normal incidence is given by $R = \left(\frac{n_1 - n_2}{n_1 + n_2}ight)^2$.

Because $n_1 
eq n_2$, $R$ is strictly greater than zero.

Consequently, the transmitted intensity $T = 1 - R$ must be strictly less than $100\%$.

This crucial detail means that on our graph, the curve for $R$ must start slightly above zero, and the curve for $T$ must start slightly below $100\%$.

### The Tipping Point: Total Internal Reflection

As we increase the angle of incidence $	heta$, the light ray tilts further away from the normal.

What happens to the intensities?

The reflected ray gets progressively stronger, while the transmitted ray gets weaker.

Eventually, we reach a very special angle called the **critical angle**, denoted by $	heta_c = \sin^{-1}\left(\frac{n_2}{n_1}ight)$.

At this exact point, something magical happens: **Total Internal Reflection (TIR)**!

The transmitted ray completely vanishes, meaning $T$ drops to exactly $0\%$.

Simultaneously, all the light energy is now reflected back into the glass, so $R$ hits a perfect $100\%$.

For any angle $	heta \ge 	heta_c$, the light remains completely trapped inside the glass, so $R$ stays at $100\%$ and $T$ stays at $0\%$.

### Decoding the Graphs

Now, let's look at our options and apply what we've learned.

We need a graph where $R$ starts above zero and $T$ starts below $100\%$ at $	heta = 0^\circ$.

We also need $R$ to smoothly reach $100\%$ and $T$ to smoothly drop to $0\%$ at the critical angle $	heta_c$, which occurs well before $90^\circ$.

If you look closely at the given options, graphs (a), (b), and (d) all incorrectly show $R$ starting at exactly $0\%$ and $T$ starting at exactly $100\%$.

Only **graph (c)** perfectly captures this beautiful physical reality, showing the correct initial values and the smooth transition to Total Internal Reflection!

Animated Solution for Physics - Optics: A light ray travelling in glass medium is incident on glass-air interface at an angle of incidence $θ$ . The reflected ( $R$ ) and transmitted ( $T$ ) intensities, both as function of $θ$ , are plotted. The correct sketch is

Select Answer:

Visualized Solution

\text{Reflection and Transmission}

\text{Normal Incidence } (\theta = 0^\circ)

\text{Increasing Angle of Incidence}

\text{Total Internal Reflection}

\text{Analyzing the Graphs}

The Sigma Insight: Refraction and Total Internal Reflection

The Boundary of Two Worlds

The Myth of Perfect Transmission

The Tipping Point

Decoding the Graphs

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