Understanding Light Bending in a Triangular Glass Prism

When a beam of white light, such as sunlight, passes through a triangular glass prism, it splits into its constituent colours. This phenomenon is known as dispersion of light. The band of colours observed is called a spectrum, commonly remembered by the acronym VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange, Red).

The bending of light as it passes from one medium to another (like air to glass or glass to air) is called refraction. The extent to which light bends depends on several factors, including the angle of incidence, the properties of the two media, and importantly, the wavelength (or colour) of the light.

Refractive Index and Bending of Light

The refractive index of a medium ($\mu$ or $n$) is a measure of how much light slows down when it enters that medium from a vacuum. It is defined as the ratio of the speed of light in vacuum ($c$) to the speed of light in the medium ($v$):

$$\mu = \frac{c}{v}$$

According to Snell's Law, when light travels from a medium with refractive index $n_1$ to a medium with refractive index $n_2$, the relationship between the angle of incidence ($\theta_1$) and the angle of refraction ($\theta_2$) is given by:

$$n_1 \sin \theta_1 = n_2 \sin \theta_2$$

For light entering a denser medium (like glass from air), $n_2 > n_1$. In this case, to maintain the equality, $\sin \theta_2 < \sin \theta_1$, which means $\theta_2 < \theta_1$. The ray bends towards the normal. The greater the ratio $n_2/n_1$, the smaller $\theta_2$ will be for a given $\theta_1$, indicating greater bending.

In the case of light passing through a prism, the amount of deviation (total bending) depends on the refractive index of the prism material for that specific colour of light. A higher refractive index for a colour means that colour bends more.

Wavelength, Speed, and Refractive Index in Glass

The speed of light in a medium like glass is dependent on its wavelength. This phenomenon is called dispersion. Different colours of light correspond to different wavelengths:

• Red light has the longest wavelength.
• Violet light has the shortest wavelength.

In dispersive materials like glass, the speed of light is lower for shorter wavelengths (violet) and higher for longer wavelengths (red). Since the refractive index is inversely proportional to the speed of light ($\mu = c/v$), this means:

• Violet light travels slower in glass, so the refractive index of glass for violet light is greatest.
• Red light travels faster in glass, so the refractive index of glass for red light is lowest.

Relating Refractive Index to Bending in a Prism

As discussed earlier, a higher refractive index leads to greater bending. Since the refractive index of glass is greatest for violet light and lowest for red light:

• Violet light bends the most when passing through the prism.
• Red light bends the least when passing through the prism.

This is why, in the spectrum obtained from a prism, violet is at one end (most deviated) and red is at the other (least deviated).

Analyzing the Options based on Light Bending and Refractive Index

Let's examine the given options:

• Option 1: Red light bends the most, as the refractive index of glass for red light is greatest. This is incorrect. Red light bends the least, and its refractive index in glass is lowest.
• Option 2: Red light bends the most, as the refractive index of glass for red light is lowest. This is incorrect. Red light bends the least, although its refractive index is lowest. The reasoning for bending the most is flawed.
• Option 3: Violet light bends the most, as the refractive index of glass for violet light is greatest. This is correct. Violet light bends the most because the refractive index of glass is highest for violet light.
• Option 4: Violet light bends the most, as the refractive index of glass for violet light is lowest. This is incorrect. Violet light does bend the most, but its refractive index in glass is greatest, not lowest. The reasoning is flawed.

Therefore, the correct statement is that violet light bends the most because the refractive index of glass for violet light is greatest.

Revision Table: Light Dispersion by Prism

Additional Information on Prism Dispersion and Light Bending

Dispersion is the phenomenon where the phase velocity of light depends on its frequency (or wavelength). This property of the medium causes different colours of light to refract at slightly different angles when entering or leaving the medium, such as a prism.

• The deviation angle ($\delta$) for a prism depends on the angle of incidence, the prism angle ($A$), and the refractive index ($\mu$). For a given prism and angle of incidence, a higher $\mu$ results in a larger deviation angle.
• White light is a mixture of different colours, each with a different wavelength and thus a different refractive index in glass. This difference in refractive index causes the separation of colours.
• Rainbows are a natural example of dispersion caused by water droplets acting like tiny prisms.

Understanding the relationship between wavelength, speed of light in a medium, refractive index, and the bending of light is fundamental to understanding optics phenomena like dispersion and refraction.