Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is $60^\circ$). In the position of minimum deviation, the angle of refraction will be Options: (A) 30° for both the colours (B) greater for the violet colour (C) greater for the red colour (D) equal but not 30° for both the colours

### The Magic of Minimum Deviation Imagine a beam of light striking a glass prism. As it enters, it bends, and as it exits, it bends again, creating a beautiful spectrum of colors. But there is a very special orientation of the prism known as the **position of minimum deviation**. When a prism is set to this magical angle, the light ray travels perfectly symmetrically through it. If you were to trace the path of the light, you would see that the refracted ray inside the prism runs exactly parallel to the base of the prism. This symmetry is the key to unlocking the problem. ### The Geometry of the Prism Because of this perfect symmetry, the angle of refraction at the first face, which we call $r_1$, is exactly equal to the angle of incidence at the second face, $r_2$. Let's simply call them both $r$. $$r_1 = r_2 = r$$ Now, from the fundamental geometry of a prism, we know that the sum of these two internal angles is always equal to the angle of the prism, denoted by $A$. $$r_1 + r_2 = A$$ Substituting our symmetric condition into this equation, we get: $$2r = A \implies r = \frac{A}{2}$$ The problem explicitly tells us that the angle of the prism $A$ is $60^\circ$. Let's substitute this value into our elegant little formula: $$r = \frac{60^\circ}{2} = 30^\circ$$ ### The Color Independence Here is where many students fall into a trap! You might think, "Wait, doesn't violet light bend more than red light because it has a higher refractive index?" Yes, violet light does bend more *in general*. However, the question specifically asks about the angle of refraction when **each color is at its own position of minimum deviation**. Look closely at our final formula: $r = \frac{A}{2}$. Do you see a refractive index $\mu$ in there? Do you see a wavelength $\lambda$? No! The angle of refraction at minimum deviation depends **only** on the physical geometry of the prism itself. Therefore, whether you are shining a red laser or a violet laser, as long as you adjust the prism to the position of minimum deviation for that specific color, the angle of refraction inside the prism will always be exactly $30^\circ$. It is a wonderful reminder that sometimes, the most complex-looking physics problems have the most beautifully simple geometric solutions!

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Animated Solution for Physics - Optics: 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

Q: What is the formula for minimum deviation?

The angle of minimum deviation $\delta_m$ is related to the refractive index by $\mu = \frac{\sin((A+\delta_m)/2)}{\sin(A/2)}$. While $\delta_m$ and $\mu$ change with color, the internal angle $r = A/2$ remains constant.

Q: What if the prism was not equilateral?

The relation $r_1 + r_2 = A$ holds for any prism. At minimum deviation, the symmetry condition $r_1 = r_2$ still applies, so $r = A/2$ is valid regardless of the prism's shape, as long as it's at minimum deviation.

Select Answer:

Visualized Solution

$Position of Minimum Deviation$

In a prism, the condition for minimum deviation occurs when the ray passes symmetrically through the prism.

$r_{1} = r_{2} = r$

By symmetry, the angle of refraction at the first face ( $r_{1}$ ) is equal to the angle of incidence at the second face ( $r_{2}$ ).

$r_{1} + r_{2} = A ⟹ r = \frac{A}{2}$

From the geometry of the prism, the sum of these internal angles is equal to the angle of the prism $A$ .

$r = \frac{6 0 ^{\circ}}{2} = 3 0^{\circ}$

Given the angle of the prism $A = 6 0^{\circ}$ .

$Independence from Wavelength$

The relation $r = \frac{A}{2}$ depends only on the angle of the prism $A$ , not on the refractive index $μ$ or the wavelength $λ$ of the light.

$Final Conclusion$

Therefore, the angle of refraction will be $3 0^{\circ}$ for both red and violet colours.

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The Sigma Insight: Refraction and Dispersion through Prism

Solution Diagram

The Magic of Minimum Deviation

Imagine a beam of light striking a glass prism. As it enters, it bends, and as it exits, it bends again, creating a beautiful spectrum of colors. But there is a very special orientation of the prism known as the position of minimum deviation.

When a prism is set to this magical angle, the light ray travels perfectly symmetrically through it. If you were to trace the path of the light, you would see that the refracted ray inside the prism runs exactly parallel to the base of the prism. This symmetry is the key to unlocking the problem.

The Geometry of the Prism

Because of this perfect symmetry, the angle of refraction at the first face, which we call

r_{1}

, is exactly equal to the angle of incidence at the second face,

r_{2}

. Let's simply call them both

r

r_{1} = r_{2} = r

Now, from the fundamental geometry of a prism, we know that the sum of these two internal angles is always equal to the angle of the prism, denoted by

A

r_{1} + r_{2} = A

Substituting our symmetric condition into this equation, we get:

2 r = A ⟹ r = \frac{A}{2}

The problem explicitly tells us that the angle of the prism

A

6 0^{\circ}

. Let's substitute this value into our elegant little formula:

r = \frac{6 0 ^{\circ}}{2} = 3 0^{\circ}

The Color Independence

Here is where many students fall into a trap! You might think, "Wait, doesn't violet light bend more than red light because it has a higher refractive index?"

Yes, violet light does bend more in general. However, the question specifically asks about the angle of refraction when each color is at its own position of minimum deviation.

Look closely at our final formula:

r = \frac{A}{2}

. Do you see a refractive index

μ

in there? Do you see a wavelength

λ

? No! The angle of refraction at minimum deviation depends only on the physical geometry of the prism itself.

Therefore, whether you are shining a red laser or a violet laser, as long as you adjust the prism to the position of minimum deviation for that specific color, the angle of refraction inside the prism will always be exactly

3 0^{\circ}

It is a wonderful reminder that sometimes, the most complex-looking physics problems have the most beautifully simple geometric solutions!

Common Traps & FAQs

Why is the ray parallel to the base at minimum deviation?

At minimum deviation, the light path through the prism is perfectly symmetrical. This symmetry forces the refracted ray inside the prism to be parallel to the base, assuming the prism is an isosceles or equilateral triangle.

Doesn't violet light bend more than red light?

Yes, violet light has a higher refractive index and bends more than red light *in general*. However, the question specifically asks about the angle of refraction *when each color is at its own position of minimum deviation*. At that specific position, the geometry dictates

r = A /2

for any color.

What is the formula for minimum deviation?

The angle of minimum deviation

δ_{m}

is related to the refractive index by

μ = \frac{s i n (( A + δ _{m} ) /2 )}{s i n ( A /2 )}

. While

δ_{m}

and

μ

change with color, the internal angle

r = A /2

remains constant.

What if the prism was not equilateral?

The relation

r_{1} + r_{2} = A

holds for any prism. At minimum deviation, the symmetry condition

r_{1} = r_{2}

still applies, so

r = A /2

is valid regardless of the prism's shape, as long as it's at minimum deviation.

How do we know

A = 6 0^{\circ}

The problem explicitly states that the angle of the prism is

6 0^{\circ}

. This is a standard value for an equilateral prism, which is commonly used in such optics experiments.

Animated Solution for Physics - Optics: 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

Select Answer:

Visualized Solution

$Position of Minimum Deviation$

$r_{1} = r_{2} = r$

$r_{1} + r_{2} = A ⟹ r = \frac{A}{2}$

$r = \frac{6 0 ^{\circ}}{2} = 3 0^{\circ}$

$Independence from Wavelength$

$Final Conclusion$

The Sigma Insight: Refraction and Dispersion through Prism

The Magic of Minimum Deviation

The Geometry of the Prism

The Color Independence

Similar Questions

The refractive index of glass is $1.520$ for red light and $1.525$ for blue light. Let $D_{1}$ and $D_{2}$ be angles of minimum deviations for red and blue light respectively in a prism of this glass. Then,

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

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).

Select Answer:

Visualized Solution

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Position of Minimum Deviation

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } r1​=r2​=r

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } r1​+r2​=A⟹r=2A​

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } r=260∘​=30∘

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Independence from Wavelength

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Final Conclusion

The Sigma Insight: Refraction and Dispersion through Prism

The Magic of Minimum Deviation

The Geometry of the Prism

The Color Independence

Similar Questions

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } For an isosceles prism of angle A and refractive index μ, it is found that the angle of minimum deviation δm​=A. Which of the following options is/are correct?

$Position of Minimum Deviation$

$r_{1} = r_{2} = r$

$r_{1} + r_{2} = A ⟹ r = \frac{A}{2}$

$r = \frac{6 0 ^{\circ}}{2} = 3 0^{\circ}$

$Independence from Wavelength$

$Final Conclusion$

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?