why cannot we obtain interference using two independent sources of light?

Interference is a fascinating phenomenon that occurs when two or more waves overlap and combine to form a new wave pattern. However, when it comes to light, not all sources can produce interference. Let's delve into why two independent sources of light typically do not lead to observable interference.

The Nature of Light Waves

Light behaves as both a wave and a particle, a concept known as wave-particle duality. When we talk about interference, we are primarily concerned with the wave aspect of light. For interference to occur, the waves must be coherent, meaning they have a constant phase relationship.

Coherence Explained

Coherence is crucial for interference. There are two types of coherence:

• Temporal Coherence: This refers to the correlation of the phase of a wave over time. A light source with a long coherence length can maintain a consistent phase relationship for a longer duration.
• Spatial Coherence: This relates to the phase correlation across different points in space. A light source that is spatially coherent can produce waves that maintain a consistent phase across a wide area.

Independent Sources and Their Limitations

When we use two independent light sources, such as two separate light bulbs, they typically emit light waves that are not coherent. This lack of coherence arises from several factors:

• Different Frequencies: Independent sources may emit light at slightly different frequencies, leading to varying wavelengths and phase relationships.
• Random Phase Relationships: Each source emits light waves that are not synchronized, resulting in random phase differences that change over time.
• Short Coherence Length: Many common light sources, like incandescent bulbs, have short coherence lengths, meaning their waves lose phase correlation quickly.

Example of Coherent Sources

To observe interference, we often use coherent sources, such as lasers. A laser emits light that is monochromatic (single wavelength) and highly coherent, allowing for stable and predictable phase relationships. When two laser beams overlap, they can create an interference pattern of bright and dark fringes on a screen, demonstrating constructive and destructive interference.

Practical Implications

In practical applications, understanding the need for coherence helps in designing experiments and technologies that rely on interference, such as holography and interferometry. These fields utilize coherent light sources to achieve precise measurements and imaging.

In summary, the inability to obtain interference from two independent light sources primarily stems from their lack of coherence. For interference to be observed, the light waves must maintain a consistent phase relationship, which is typically not the case with independent sources. Instead, coherent sources like lasers are essential for producing clear and observable interference patterns.