In the dispersion of white light by a common glass prism, which one among the following is correct?
Blue light deviates the most because blue light has lowest speed in prism
Understanding Light Dispersion by a Prism
When a beam of white light passes through a transparent medium like a glass prism, it splits into its constituent colors. This phenomenon is known as dispersion of light. The band of colors produced is called the spectrum of white light, commonly remembered by the acronym VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange, Red).
Each color of light is associated with a specific wavelength and frequency. In vacuum, all colors of light travel at the same speed, the speed of light 'c'. However, when light enters a different medium like glass, its speed changes, and this speed is different for different colors. The speed of light in a medium is related to the refractive index ($\mu$) of the medium for that color by the formula:
\(\mu = \frac{c}{v}\)
where \(v\) is the speed of light in the medium and \(c\) is the speed of light in vacuum.
This equation shows that the refractive index of a medium for a specific color is inversely proportional to the speed of that color in the medium. A higher refractive index means a lower speed in the medium.
Deviation of Light in a Prism
When light passes through a prism, it undergoes refraction at two surfaces. The amount by which a color of light bends (deviates) depends on the angle of incidence and the refractive index of the prism material for that specific color. For a given angle of incidence and prism, a higher refractive index results in a greater deviation.
So, the amount of deviation for a color is directly related to the refractive index of the prism for that color:
Deviation \(\propto \mu\)
Refractive Index and Wavelength
The refractive index of a material is not constant for all colors (wavelengths) of light. It generally varies with wavelength. For transparent materials like glass, the refractive index is higher for shorter wavelengths and lower for longer wavelengths. In the visible spectrum, violet light has the shortest wavelength, and red light has the longest wavelength.
This means that for glass:
- Refractive index for violet light > Refractive index for blue light > ... > Refractive index for red light.
- \(\mu_{violet} > \mu_{blue} > ... > \mu_{red}\)
Connecting Speed, Refractive Index, and Deviation
Combining the relationships discussed:
- Speed of light in a medium is inversely proportional to the refractive index (\(v \propto 1/\mu\)).
- Deviation in a prism is directly proportional to the refractive index (Deviation \(\propto \mu\)).
Therefore, we can conclude:
- A higher refractive index means lower speed and greater deviation.
- A lower refractive index means higher speed and smaller deviation.
Applying this to the colors in the spectrum passing through a glass prism:
- Blue light has a shorter wavelength than red light.
- Therefore, the refractive index of glass for blue light is higher than for red light (\(\mu_{blue} > \mu_{red}\)).
- Since \(\mu_{blue} > \mu_{red}\), the speed of blue light in glass is lower than the speed of red light (\(v_{blue} < v_{red}\)).
- Since \(\mu_{blue} > \mu_{red}\), blue light deviates more than red light when passing through the prism.
Red light, having the longest wavelength, has the lowest refractive index in glass, the highest speed, and thus deviates the least. Violet light, having the shortest wavelength, has the highest refractive index, the lowest speed, and deviates the most. Blue light is close to the violet end of the spectrum.
Analyzing the Options
- Option 1: Red light deviates the most because red light has highest speed in prism. This is incorrect. Red light deviates the least. While red light does have the highest speed in the prism, this high speed results in the *least* deviation.
- Option 2: Blue light deviates the most because blue light has highest speed in prism. This is incorrect. Blue light does deviate the most (among the common colors like red/blue), but it has the *lowest* speed in the prism, not the highest.
- Option 3: Red light deviates the most because red light has lowest speed in prism. This is incorrect. Red light deviates the least. While lowest speed would result in the most deviation, red light has the *highest* speed in the prism.
- Option 4: Blue light deviates the most because blue light has lowest speed in prism. This is correct. Blue light deviates the most (more than red) because the refractive index for blue light in glass is higher, which means the speed of blue light in glass is lower than other colors like red.
| Property | Red Light | Blue Light |
|---|---|---|
| Wavelength (\(\lambda\)) | Longest | Shorter |
| Speed in Glass (\(v\)) | Highest | Lowest |
| Refractive Index (\(\mu\)) | Lowest | Highest |
| Deviation by Prism | Least | Most |
Conclusion
In the dispersion of white light by a common glass prism, blue light deviates the most among the options provided because the refractive index of the glass is highest for blue light, leading to the lowest speed of blue light in the prism.
Revision Table: Dispersion of Light Concepts
| Concept | Explanation |
|---|---|
| Dispersion | Splitting of white light into its constituent colors when passing through a transparent medium due to different speeds of different colors. |
| Spectrum | The band of colors (VIBGYOR) produced by dispersion. |
| Refractive Index (\(\mu\)) | A property of a medium that determines how much light slows down when entering it (\(\mu = c/v\)). It varies with wavelength for different colors. |
| Deviation Angle | The change in direction of a light ray after passing through a prism. It depends on the prism angle and refractive index. Higher refractive index means greater deviation. |
| Wavelength and Refractive Index | In transparent media like glass, shorter wavelengths have higher refractive indices (\(\mu\)) and longer wavelengths have lower \(\mu\). |
| Speed and Refractive Index | Speed of light in a medium (\(v\)) is inversely proportional to the refractive index (\(\mu\)). \(v \propto 1/\mu\). |
| Deviation and Speed | Lower speed in the medium leads to higher refractive index and thus greater deviation. |
Additional Information: Causes of Dispersion and Applications
Dispersion occurs because the interaction of light with the electrons in the material depends on the frequency (and thus wavelength) of the light. This frequency-dependent interaction causes the speed of light (and hence the refractive index) to vary with color. This phenomenon is called chromatic dispersion.
Violet light (shortest wavelength, highest frequency) interacts more strongly than red light (longest wavelength, lowest frequency), causing it to slow down more and thus having a higher refractive index and greater deviation.
Applications of dispersion include:
- Prisms used in spectroscopes to analyze the composition of light sources.
- Formation of rainbows (dispersion by raindrops).
- Chromatic aberration in lenses (different colors focusing at slightly different points, often corrected in optical instruments).
It is important to remember that in vacuum, all colors travel at the same speed, and there is no dispersion.
Important Questions from Diffraction
In a double-slit experiment, when light of wavelength $\text{600 nm}$ is used, the central maximum and the second bright fringe are separated by $\text{3 mm}$ on a screen placed $\text{1.5 m}$ away. If the entire apparatus is then immersed in a liquid with a refractive index of $\text{1.5}$, what will be the angular separation between the first and fourth dark fringes?
Which one of the following statements about X-rays is not true?
When light passes from air to water, the angle of refraction is:
The primary rainbow appears after the rain is due to
The colour of the fast rotating Newton's Disc, appears to be
