The angle of deviation through a prism is minimum when
A. incident ray and emergent ray are symmetri

Q: Why is the refracted ray parallel to the base only for minimum deviation?

For minimum deviation, the ray path is symmetric. In an isosceles or equilateral prism, this symmetry forces the refracted ray to be parallel to the base. If it weren't parallel, reversing the ray would give a different path with the same deviation, contradicting the uniqueness of the minimum.

Q: Does this hold true for all prisms?

The condition $i = e$ holds for minimum deviation in all prisms. However, the refracted ray is parallel to the base specifically for prisms where the two refracting faces are symmetric with respect to the base (like equilateral or isosceles prisms).

Q: What happens if $i \neq e$?

If the angle of incidence is not equal to the angle of emergence, the deviation is not at its minimum. There will be two different angles of incidence that produce the same angle of deviation.

Q: Why is statement D incorrect?

Statement D claims $e = 2i$. We have already established that for minimum deviation, $e = i$. Therefore, $e$ cannot be $2i$ unless both are zero, which is not the case here.

Q: How does the principle of reversibility apply here?

The principle of reversibility states that if you reverse the direction of light, it retraces its path. If $i \neq e$ produced minimum deviation, reversing the ray would mean entering at $e$ and exiting at $i$, giving the same minimum deviation at two different incidence angles. But the minimum is unique, so $i$ must equal $e$.

Question

The angle of deviation through a prism is minimum when
A. incident ray and emergent ray are symmetric to the prism
B. the refracted ray inside the prism becomes parallel to its base
C. angle of incidence is equal to that of the angle of emergence
D. angle of emergence is double the angle of incidence
Choose the correct answer from the options given below.

Options:

(A) Statements (A), (B) and (C) are true.

(B) Only statement (D) is true.

(C) Only statements (A) and (B) are true.

(D) Statements (B) and (C) are true.

Sigma Percentile · Accepted Answer

### The Journey of a Light Ray

Imagine a single ray of light traveling through the air and striking the smooth, angled surface of a glass prism. As it enters this denser medium, it slows down and bends—a phenomenon we know as refraction. It travels through the glass and then hits the second surface, bending once again as it exits back into the air.

This double bending causes the light ray to deviate from its original path. If we were to trace the original path forward and the final path backward, the angle at which they intersect is called the **angle of deviation**, denoted by $\delta$.

### The Magic of Symmetry

Now, physicists love finding minimums and maximums. If we slowly change the angle at which the light hits the prism (the angle of incidence, $i$), the angle of deviation $\delta$ also changes. It turns out that there is one specific angle of incidence where the deviation is at its absolute minimum, $\delta_m$.

What is so special about this point? **Symmetry**.

At the angle of minimum deviation, the light ray passes through the prism perfectly symmetrically. This symmetry leads to two beautiful geometric consequences:
1. The angle at which the light enters the prism is exactly equal to the angle at which it leaves. In mathematical terms, the angle of incidence equals the angle of emergence ($i = e$).
2. Because of this perfect balance, the refracted ray traveling inside the prism becomes perfectly parallel to the base of the prism (assuming the prism is isosceles or equilateral).

### Decoding the Statements

Armed with this conceptual clarity, let's evaluate the statements given in the problem:
*   **Statement A:** "Incident ray and emergent ray are symmetric to the prism." This is the very definition of the minimum deviation condition. **(True)**
*   **Statement B:** "The refracted ray inside the prism becomes parallel to its base." As we just discussed, this is a direct consequence of the symmetry. **(True)**
*   **Statement C:** "Angle of incidence is equal to that of the angle of emergence." This is the mathematical expression of the symmetry ($i = e$). **(True)**
*   **Statement D:** "Angle of emergence is double the angle of incidence." Since we know $i = e$, this statement is clearly incorrect. **(False)**

Therefore, statements A, B, and C are all correct, making the first option the right choice.

Select Answer:

Visualized Solution

The Phenomenon of Deviation

Condition for Minimum Deviation

Symmetry Implications

Evaluating the Statements

Final Conclusion

The Sigma Insight: Refraction and Dispersion through Prism

The Journey of a Light Ray

The Magic of Symmetry

Decoding the Statements

Similar Questions

For an isosceles prism of angle $A$ and refractive index $μ$ , it is found that the angle of minimum deviation $δ_{m} = A$ . Which of the following options is/are correct?

A ray of light passing through a prism ( $μ = 3$ ) suffers minimum deviation. It is found that the angle of incidence is double the angle of refraction within the prism. Then, the angle of prism is ……… (in degrees).

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 ?

Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is $6 0^{\circ}$ ). In the position of minimum deviation, the angle of refraction will be

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

Monochromatic light is incident on a glass prism of angle $A$ . If the refractive index of the material of the prism is $μ$ , a ray incident at an angle $θ$ , on the face $A B$ would get transmitted through the face $A C$ of the prism provided