A given ray of light suffers minimum deviation in an equilateral prism P. Additional prisms Q and R

Q: Why doesn't the ray bend when it goes from prism P to prism Q?

Bending (refraction) only occurs when there is a change in the refractive index. Since prisms P and Q are made of the exact same material, the light ray doesn't "see" a boundary. It travels straight through as if it were a single solid block of glass.

Q: Does the size of the prism affect the angle of deviation?

No! The angle of deviation depends only on the angle of incidence, the refracting angle of the prism ($A$), and the refractive index ($\mu$). The physical size or thickness of the prism has absolutely no effect on the deviation angle.

Q: What if prism Q was made of a different material?

If prism Q had a different refractive index, the ray would bend at the P-Q interface and again at the Q-R interface. The problem would become much more complex, and the final deviation would definitely change.

Q: Why is the ray parallel to the base inside prism P?

The problem states the ray suffers *minimum deviation*. In an equilateral (or any symmetric) prism, minimum deviation occurs when the ray passes symmetrically through the prism, which means it travels perfectly parallel to the base.

Q: Could the ray suffer total internal reflection at the Q-R interface?

Total internal reflection can only happen when light travels from a denser medium to a rarer medium. Since Q and R have the same refractive index, the relative refractive index is 1, so total internal reflection is impossible at that specific interface.

Question

A given ray of light suffers minimum deviation in an equilateral prism $P$. Additional prisms $Q$ and $R$ of identical shape and of the same material as $P$ are now added as shown in the figure. The ray will suffer

Options:

(A) greater deviation

(B) no deviation

(C) same deviation as before

(D) total internal reflection

Sigma Percentile · Accepted Answer

### Analyzing the Setup

Imagine a single ray of light entering an equilateral prism, $P$. We are told a very specific piece of information: the ray suffers **minimum deviation**.

What does this physically mean? In any symmetric prism, minimum deviation occurs when the light ray travels perfectly symmetrically through it.

Geometrically, this means the ray inside the prism travels **parallel to the base**. Furthermore, the angle at which the ray enters the prism (angle of incidence, $i$) is exactly equal to the angle at which it leaves (angle of emergence, $e$).

### The Illusion of Complexity

Now, the problem introduces a twist. We place two more identical prisms, $Q$ and $R$, right next to $P$. Prism $Q$ is inverted, and prism $R$ is upright.

At first glance, this looks like a complex multi-prism problem where we need to apply Snell's Law at every single boundary. But let's pause and think about the physics of refraction.

Refraction, or the bending of light, only happens when light crosses a boundary between two media with **different refractive indices**.

Since prisms $P$, $Q$, and $R$ are made of the exact same material, the interfaces between them are optically invisible! The light ray doesn't "know" it's passing from prism $P$ to prism $Q$. It just sees a continuous block of glass.

### The Giant Prism Equivalence

Because the internal boundaries don't affect the light, we can treat the entire combination of $P$, $Q$, and $R$ as a single, solid piece of glass.

Look at the outer boundaries of this combined shape. The ray enters through the left face of $P$ and exits through the right face of $R$.

If we extend these two refracting faces upwards, they meet at an angle of $60^\circ$. This means our combination of three small prisms is optically equivalent to one **giant equilateral prism**!

### The Final Verdict

The angle of deviation $\delta$ produced by a prism is given by the formula:
$$ \delta = i + e - A $$

This deviation depends only on three factors:
1. The angle of incidence ($i$)
2. The refracting angle of the prism ($A$)
3. The refractive index of the material ($\mu$)

Notice what is missing from this list? The **size** of the prism!

Since the angle of incidence is the same, the effective refracting angle $A$ is still $60^\circ$, and the material $\mu$ is unchanged, the ray will experience the exact same bending.

Therefore, the ray will suffer the **same deviation as before**.

Animated Solution for Physics - Optics: A given ray of light suffers minimum deviation in an equilateral prism $P$ . Additional prisms $Q$ and $R$ of identical shape and of the same material as $P$ are now added as shown in the figure. The ray will suffer

Select Answer:

Visualized Solution

$Minimum Deviation in Prism P$

$Adding Prisms Q and R$

$The Equivalent Giant Prism$

$Deviation Remains Unchanged$

$Conclusion$

The Sigma Insight: Refraction and Dispersion through Prism

Analyzing the Setup

The Illusion of Complexity

The Giant Prism Equivalence

The Final Verdict

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