Question

Wave light travels from an optically rarer medium to an optically denser medium its velocity decrease because of change in (A) frequency (B) wavelength (C) amplitude (D) phase

Short answer

The correct answer is (B) wavelength. The wavelength of the light wave decreases when traveling from an optically rarer medium to an optically denser medium, causing the velocity to decrease as well.

Step-by-step solution

Recall Snell's Law and the Wave Equation

Snell's law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities of light in the two media. \[n_1 \times \sin{\theta_1} = n_2 \times \sin{\theta_2}\] where \(n_1\) and \(n_2\) are the refractive indices of the rarer and denser media, and \(\theta_1\) and \(\theta_2\) are the angles of incidence and refraction. The wave equation relates the velocity (\(v\)), frequency (\(f\)), and wavelength (\(\lambda\)) of a wave: \[v = f \lambda\]

Analyze the effect on frequency

The frequency of the wave does not change when light passes from one medium to another. This is because the frequency depends on the source of light, and not on the medium through which the light is transmitted.

Analyze the effect on wavelength

Wavelength (\(\lambda\)) is the distance between two successive crests or troughs in a wave. As the velocity of light decreases when it enters an optically denser medium, the wavelength also decreases. This can be seen from the wave equation: \[\lambda = \frac{v}{f}\] The frequency (\(f\)) remains constant, but the velocity (\(v\)) decreases, so the wavelength (\(\lambda\)) also decreases.

Analyze the effect on amplitude

Amplitude is the maximum displacement of a point on a wave from its equilibrium position. The amplitude of the wave does not change when light passes from one medium to another. This is because the amplitude depends on the energy of the wave, and not on the medium through which the light is transmitted.

Analyze the effect on phase

Phase is the position of a point in time on a waveform cycle. Although the phase of the light wave changes as it enters a denser medium, this is not the cause of the decrease in velocity.

Choose the correct answer

According to our analysis, the correct answer is (B) wavelength. The wavelength of the light wave decreases when traveling from an optically rarer medium to an optically denser medium, causing the velocity to decrease as well.

Key concepts

Optically Denser Medium

When we talk about an optically denser medium, we refer to a medium where light travels slower compared to another medium. This concept is critical in understanding how light behaves as it moves from one material to another. In optical terms, the density does not refer to physical density but to the ability of the medium to slow down the light wave. For example, glass is an optically denser medium compared to air.

As light enters a denser medium from a less dense one, several things happen:

• The speed of light decreases, affecting other properties of the wave.
• The light wave bends towards the normal line—a concept explained by Snell's Law.
• This bending and slowing down is what characterizes the medium as 'optically denser.'

Understanding the nature of an optically denser medium helps explain many optical phenomena like refraction and internal reflections.

Wave Equation

The wave equation is an essential tool in physics for understanding wave behaviors. It shows the relationship between velocity, frequency, and wavelength of a wave:
\[ v = f \lambda \] Where \( v \) is the velocity, \( f \) is the frequency, and \( \lambda \) is the wavelength.

As a light wave enters an optically denser medium, its velocity \( v \) decreases, while its frequency \( f \) remains constant. This results in a change in wavelength \( \lambda \).

• The wavelength becomes shorter as velocity decreases but the frequency stays unaffected.
• This equation supports the idea that only the wavelength changes when a wave enters a different medium.

This relationship is a cornerstone in understanding how light behaves across various media.

Light Wave Behavior

Light wave behavior changes significantly when moving between different media. Upon entering an optically denser medium:

• The velocity of the wave decreases.
• The wavelength also decreases, as indicated by the wave equation.
• The light wave bends, changing its direction as per Snell's Law.

Each of these changes occurs due to the intrinsic properties of the movement among different media.

Despite these changes, it's crucial to note that certain properties remain constant, such as:

• Frequency, which is determined by the light source and stays the same irrespective of the medium.
• Amplitude, since it depends on the wave's energy, not the medium it traverses.

This explains why, while light behavior can seem complex, fundamental constant properties help in predicting outcomes.

Refractive Index

The refractive index measures how much the speed of light is reduced inside a medium. It is represented as a ratio in Snell's Law of Refraction. For two media, the refractive index \( n \) relates to how strongly a medium can bend the light rays:\[ n = \frac{c}{v} \]Where \( c \) is the speed of light in a vacuum, and \( v \) is the speed of light in the medium.

When light enters a denser medium:

• The refractive index is higher than that of the medium it came from.
• The angle of refraction becomes smaller than the angle of incidence, reflecting the bending of light.

This measure helps explain why light slows down and bends. A higher refractive index means greater optical density, leading to more significant bending and slower propagation of light in the medium.

Both practical and theoretical investigations of refractive indices help explain numerous optical phenomena and applications, from lenses to fiber optics.