A ray of light is incident on an equilateral glass prism placed on a horizontal table. For minimum d

Q: Why does minimum deviation imply a symmetric path?

By the principle of reversibility of light, if the ray wasn't symmetric, reversing its path would give a different angle of incidence with the exact same minimum deviation. However, experimental and mathematical proofs show there is only one unique angle of incidence for minimum deviation. Thus, the path must be symmetric ($i = e$).

Q: Is the internal ray always parallel to the base for minimum deviation?

It is parallel to the base only if the prism is an isosceles or equilateral prism where the two refracting faces make equal angles with the base. Since an equilateral prism is highly symmetric, this condition holds perfectly.

Q: What if the prism was not equilateral?

If the prism was scalene (all sides unequal), the ray would still pass symmetrically with respect to the refracting angle at the top, but it would not necessarily be parallel to the third face (the base).

Q: Does the refractive index of the prism affect this geometric property?

No, the geometric symmetry at minimum deviation holds true regardless of the refractive index of the material, as long as the prism itself is geometrically symmetric.

Q: Why can't PQ or RS be horizontal?

PQ and RS are the incident and emergent rays. For them to be horizontal, the angle of incidence would have to perfectly match the slant of the prism faces. While possible for a specific refractive index, it is not a general rule, whereas QR being horizontal is a guaranteed geometric consequence of minimum deviation in this setup.

Question

A ray of light is incident on an equilateral glass prism placed on a horizontal table. For minimum deviation which of the following is true ?

Options:

(A) PQ is horizontal

(B) QR is horizontal

(C) RS is horizontal

(D) Either PQ or RS is horizontal

Sigma Percentile · Accepted Answer

This problem is a beautiful demonstration of how physical principles manifest as elegant geometric properties. Let's embark on a journey to understand the behavior of light as it passes through a prism, specifically focusing on the fascinating state of **minimum deviation**.

### Analyzing the Setup

Imagine a light ray traveling through the air and striking the face of an equilateral glass prism. As it enters the denser glass medium, it bends towards the normal—this is the incident ray, denoted as $PQ$. Inside the prism, the ray travels along the path $QR$. Finally, as it exits the prism back into the air, it bends away from the normal, forming the emergent ray $RS$.

In general, the path of the ray is asymmetric. The angle at which it enters ($i$) is different from the angle at which it leaves ($e$). However, there is a unique, special angle of incidence where the total deviation of the ray is at its absolute minimum.

### The Magic of Minimum Deviation

When a light ray undergoes **minimum deviation**, a profound symmetry emerges. Nature loves symmetry! In this state, the light ray passes through the prism perfectly symmetrically.

Mathematically, this means the angle of incidence is exactly equal to the angle of emergence:

$i = e$

Consequently, the angles of refraction at the two internal faces are also equal:

$r_1 = r_2$

### The Geometric Consequence

Because our prism is an **equilateral prism** (meaning all its angles are $60^\circ$ and it is perfectly symmetric), this internal symmetry of the light ray has a direct geometric consequence. The refracted ray inside the prism, $QR$, aligns itself to be perfectly parallel to the base of the prism.

$QR \parallel 	ext{Base}$

### Final Conclusion

The problem explicitly states that the prism is placed on a **horizontal table**. This means the base of the prism is perfectly horizontal.

Since we have established that the internal ray $QR$ is parallel to the base during minimum deviation, it inescapably follows that $QR$ must also be horizontal.

Therefore, the correct statement is that **$QR$ is horizontal**, making option (b) the right choice. It is a simple, logical deduction that beautifully connects the physics of refraction with pure geometry.

Animated Solution for Physics - Optics: A ray of light is incident on an equilateral glass prism placed on a horizontal table. For minimum deviation which of the following is true ?

Select Answer:

Visualized Solution

\text{Condition for Minimum Deviation}

\text{Symmetry in Equilateral Prism}

\text{Conclusion}

The Sigma Insight: Refraction and Dispersion through Prism

Analyzing the Setup

The Magic of Minimum Deviation

The Geometric Consequence

Final Conclusion

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