91Ó°ÊÓ

A cross section of a scale from the wing of a blue morpho butterfly reveals the source of the butterfly's color. As Figure \(\mathrm{P} 17.69 \mathrm{b}\) shows, the scales are covered with structures that look like small Christmas trees. Light striking the wings reflects from different layers of these structures, and the differing path lengths cause the reflected light to interfere constructively or destructively, depending on the wavelength. For light at normal incidence, blue light experiences constructive interference while other colors undergo destructive interference and cancel. Acetone fills the spaces in the scales with a fluid of index of refraction \(n=1.38 ;\) this changes the conditions for constructive interference and results in a change in color. The change in color when acetone is placed on the wing is due to the difference between the indices of refraction of acetone and air. Consider light of some particular color. In acetone, A. The frequency of the light is less than in air. B. The frequency of the light is greater than in air. C. The wavelength of the light is less than in air. D. The wavelength of the light is greater than in air.

Step by step solution

01

Understanding light interference, refraction, and frequency

To solve this, understanding that when light moves from one medium to another, the speed of light changes, but the frequency remains the same is important. This is because frequency is a property of the source of light (in this case the incident light) and doesn't change with medium.

02

Relating speed, frequency and wavelength

The speed of light in a medium is given by the equation \(v=fλ\), where \(v\) is the speed of light, \(f\) is its frequency and \(λ\) its wavelength. Since the frequency remains constant when light moves from one medium (air in this case) to another (like acetone), if the speed of light decreases as it does when moving from air (lower refractive index) to acetone (higher refractive index), the wavelength must also decrease to satisfy the equation.

03

Reaching the conclusion

Based on the analysis and the relationship between frequency, wavelength and speed of light when light moves from a medium of lower refractive index (air) to a medium of higher refractive index (acetone), it can be deduced that: The frequency of light doesn't change, but the wavelength in acetone is less than in air.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Light Interference

Light interference refers to the phenomenon where two or more light waves overlap, resulting in a new wave pattern. When light waves meet, they can combine to create regions of increased intensity or cancel each other out, leading to areas of reduced intensity.
These interactions depend on the phase relationship between the overlapping waves. For instance:

• Constructive interference: Occurs when the peaks of one wave align with the peaks of another, enhancing the overall brightness or color.
• Destructive interference: Happens when the peaks of one wave align with the troughs of another, effectively cancelling each other out, leading to reduced brightness or the absence of specific colors.

Understanding light interference is essential when analyzing phenomena like the iridescent colors of a blue morpho butterfly's wings or soap bubbles.

Refractive Index

The refractive index is a dimensionless number that indicates how much the speed of light is reduced within a medium compared to the speed in a vacuum. Represented by the symbol \(n\), it shows how light bends as it passes from one medium to another.
A higher refractive index means that light slows down more when entering the medium.

• For air, the refractive index is approximately 1, meaning light travels almost as fast in air as it does in a vacuum.
• Acetone has a refractive index of approximately 1.38, meaning light travels slower in acetone compared to air.

This slowing down affects how light waves overlap, influencing interference patterns and consequently, the visible colors.

Wavelength

Wavelength refers to the distance between successive peaks (or troughs) of a wave. It determines many properties of light, including its color in the visible spectrum.
When light moves through different media, its speed and wavelength change, but its frequency remains constant.

• In media with higher refractive indices, like acetone, the wavelength of light decreases as compared to air.
• This change in wavelength affects interference patterns, shifting the colors perceived under different viewing conditions.

Understanding wavelength adjustment is crucial for explaining why the color of the blue morpho butterfly's wings change when immersed in acetone.

Frequency

Frequency is the number of times a wave cycle passes a point per unit time. It is measured in hertz (Hz) and remains constant when light transitions between different media. This is because frequency is fundamentally tied to the source of the light wave.
Regardless of the medium,

• Frequency remains unchanged, although speed and wavelength do alter.
• This constancy ensures that the color (which is dependent on frequency) remains the same even if the wave's speed or wavelength is modified by different media.

Keeping the frequency in focus helps to predict how light behaves across various materials without altering its inherent color properties.

Constructive and Destructive Interference

Constructive and destructive interference explains how overlapping light waves can produce regions of varying brightness and color.
These phenomena depend on the phase differences between interacting waves:

• Constructive interference: Occurs when two wave crests meet, amplifying the intensity and creating a vibrant color (like the blue in a butterfly wing).
• Destructive interference: Takes place when a wave crest and a trough meet, reducing intensity, leading to muted or absent colors.

In practical applications, these principles are harnessed in technology ranging from noise-cancelling headphones to optical coatings, illustrating their wide-ranging importance across different fields of physics and engineering.