Which two rays interfere to give interference in Newton rings?
2 Answers
Newton's rings are a classic example of interference patterns caused by the division of amplitude. The two rays that interfere to produce the characteristic concentric rings in Newton's rings are as follows:
1. **The Ray Reflected from the Top Surface of the Thin Film (Air):**
- This ray is reflected directly at the curved surface of the lens in contact with the flat glass plate below.
- This reflection occurs at the interface between the air layer (thin film) and the lens, where light travels from a medium of lower refractive index (air) to a higher refractive index (glass).
2. **The Ray Reflected from the Bottom Surface of the Thin Film (Air):**
- This ray is transmitted through the thin air film, reaches the flat glass surface below, and is then reflected back upward.
- This reflection occurs at the interface between the air and the flat glass plate, where light travels from a lower refractive index (air) to a higher refractive index (glass).
### Interference Mechanism:
- The two reflected rays recombine and interfere, resulting in constructive or destructive interference depending on their phase difference.
- The phase difference arises due to:
1. **Path Difference:** The extra distance traveled by the second ray through the air film.
2. **Phase Change Upon Reflection:** A phase change of \(\pi\) (or half a wavelength) occurs when the first ray is reflected at the lens-air interface (from a medium of lower to higher refractive index). No phase change occurs when the second ray is reflected at the air-glass interface (from a medium of higher to lower refractive index).
### Resulting Pattern:
- **Bright Rings (Constructive Interference):** When the total phase difference (path difference and phase shift) is an integral multiple of \(2\pi\).
- **Dark Rings (Destructive Interference):** When the total phase difference is an odd multiple of \(\pi\).
### Key Note:
The air film's varying thickness due to the curvature of the lens creates the concentric ring pattern, with each fringe corresponding to a specific thickness of the air layer.
1. **The Ray Reflected from the Top Surface of the Thin Film (Air):**
- This ray is reflected directly at the curved surface of the lens in contact with the flat glass plate below.
- This reflection occurs at the interface between the air layer (thin film) and the lens, where light travels from a medium of lower refractive index (air) to a higher refractive index (glass).
2. **The Ray Reflected from the Bottom Surface of the Thin Film (Air):**
- This ray is transmitted through the thin air film, reaches the flat glass surface below, and is then reflected back upward.
- This reflection occurs at the interface between the air and the flat glass plate, where light travels from a lower refractive index (air) to a higher refractive index (glass).
### Interference Mechanism:
- The two reflected rays recombine and interfere, resulting in constructive or destructive interference depending on their phase difference.
- The phase difference arises due to:
1. **Path Difference:** The extra distance traveled by the second ray through the air film.
2. **Phase Change Upon Reflection:** A phase change of \(\pi\) (or half a wavelength) occurs when the first ray is reflected at the lens-air interface (from a medium of lower to higher refractive index). No phase change occurs when the second ray is reflected at the air-glass interface (from a medium of higher to lower refractive index).
### Resulting Pattern:
- **Bright Rings (Constructive Interference):** When the total phase difference (path difference and phase shift) is an integral multiple of \(2\pi\).
- **Dark Rings (Destructive Interference):** When the total phase difference is an odd multiple of \(\pi\).
### Key Note:
The air film's varying thickness due to the curvature of the lens creates the concentric ring pattern, with each fringe corresponding to a specific thickness of the air layer.
Newton's rings are a classic interference phenomenon observed when a plano-convex lens is placed on a flat glass surface. The interference is produced due to the superposition of two specific rays of light:
1. **Ray 1: Reflected from the lower surface of the lens (convex surface)**
When light falls on the curved surface of the lens, part of it gets reflected at the interface between the lens and the thin air gap beneath it.
2. **Ray 2: Reflected from the upper surface of the flat glass plate**
The remaining light transmits through the thin air gap and reflects from the flat glass surface beneath the lens.
### How Interference Occurs:
- The two rays described above travel slightly different optical paths due to the varying thickness of the air gap between the lens and the glass plate.
- As these two reflected rays recombine, they interfere constructively or destructively depending on the path difference between them. This path difference arises because the thickness of the air gap changes radially outward from the point of contact between the lens and the glass plate.
### Conditions for Interference:
- **Constructive Interference (Bright Rings):** Occurs when the path difference is an integral multiple of the wavelength of light (\(2t = m\lambda\), where \(m = 0, 1, 2, \dots\)).
- **Destructive Interference (Dark Rings):** Occurs when the path difference is a half-integral multiple of the wavelength (\(2t = (m + 0.5)\lambda\), where \(m = 0, 1, 2, \dots\)).
Here, \(t\) is the thickness of the air gap at a particular point, and \(\lambda\) is the wavelength of light used.
### Additional Notes:
- A phase change of \(\pi\) (or half a wavelength) occurs at the reflection from the denser medium (flat glass plate). This phase shift must be accounted for in determining the interference condition.
- The result is a pattern of concentric rings of alternating bright and dark fringes, called **Newton's Rings**.
This interference phenomenon illustrates the wave nature of light and is a valuable method to measure the wavelength of light or determine the refractive index of thin films.
1. **Ray 1: Reflected from the lower surface of the lens (convex surface)**
When light falls on the curved surface of the lens, part of it gets reflected at the interface between the lens and the thin air gap beneath it.
2. **Ray 2: Reflected from the upper surface of the flat glass plate**
The remaining light transmits through the thin air gap and reflects from the flat glass surface beneath the lens.
### How Interference Occurs:
- The two rays described above travel slightly different optical paths due to the varying thickness of the air gap between the lens and the glass plate.
- As these two reflected rays recombine, they interfere constructively or destructively depending on the path difference between them. This path difference arises because the thickness of the air gap changes radially outward from the point of contact between the lens and the glass plate.
### Conditions for Interference:
- **Constructive Interference (Bright Rings):** Occurs when the path difference is an integral multiple of the wavelength of light (\(2t = m\lambda\), where \(m = 0, 1, 2, \dots\)).
- **Destructive Interference (Dark Rings):** Occurs when the path difference is a half-integral multiple of the wavelength (\(2t = (m + 0.5)\lambda\), where \(m = 0, 1, 2, \dots\)).
Here, \(t\) is the thickness of the air gap at a particular point, and \(\lambda\) is the wavelength of light used.
### Additional Notes:
- A phase change of \(\pi\) (or half a wavelength) occurs at the reflection from the denser medium (flat glass plate). This phase shift must be accounted for in determining the interference condition.
- The result is a pattern of concentric rings of alternating bright and dark fringes, called **Newton's Rings**.
This interference phenomenon illustrates the wave nature of light and is a valuable method to measure the wavelength of light or determine the refractive index of thin films.