Problem 67 - Master Resource Book in JEE Main Physics

Question

In a Young's double slit experiment, the source is white light. One of the holes is covered by a red filter and another by a blue filter. In this case (a) there should be no interference fringe (b) there should be an interference pattern for red mixing with one for blue (c) there should be altemate interference patterns of red and blue (d) None of the above

Step-by-Step Solution

Answer

(d) None of the above.

Step 1: Understand the Experiment

A Young's double slit experiment involves light passing through two closely spaced slits to create an interference pattern on a screen. Each slit acts as a source of light waves that spread out and combine to form the pattern, showing constructive and destructive interference.

Step 2: Analyze the Effects of Filters

In this scenario, a red filter covers one slit, allowing only red light through, while a blue filter covers the other slit, allowing only blue light through. These filters ensure that each slit emits light of different wavelengths.

Step 3: Determine Possibility of Interference

For interference to occur, the light waves need to be coherent, meaning they must have a constant phase relationship, which is typical when they are of the same wavelength. Here, one slit emits red light and the other emits blue light, making them incoherent.

Step 4: Evaluate the Options Given

(a) There should be no interference fringe: This suggests no visible pattern due to incoherence. (b) An interference pattern for red mixing with one for blue: This implies mixture, which isn't possible due to incoherence. (c) Alternate patterns of red and blue: Predicts visible alternating patterns, which can't happen with incoherent sources. None of the choices describe the situation correctly. (d) None of the above: Evaluating previous steps indicates that none accurately describe what happens.

Key Concepts

Interference Pattern

An interference pattern is a series of bright and dark bands or lines created when waves overlap, such as light waves. This happens when light from two sources, like the slits in Young's double slit experiment, overlap and interfere with one another.

Interference can be constructive or destructive:

• Constructive interference: When waves align such that their peaks and troughs match, they add together, resulting in bright bands.
• Destructive interference: When waves are out of phase and their peaks and troughs do not align, they cancel each other out, resulting in dark bands.

In Young's experiment, this pattern is observed on a screen and appears as alternating dark and bright fringes. The presence of an interference pattern indicates that the light is behaving like a wave, rather than just a particle. It's key for visualizing wave behavior in everyday physics applications.

Coherent Light

Coherent light means that the light waves maintain a constant phase relationship. This is essential for producing clear and stable interference patterns. When thinking about coherence, picture synchronized dancers who move in step perfectly.

In physics, coherence ensures that:

• Light waves have the same frequency.
• Light waves have a stable relative phase over time.

In Young’s double slit experiment, coherence is necessary for the distinct interference patterns to form. Without coherence, light waves won't align correctly, preventing constructive or destructive interference from occurring consistently. This is why in the exercise where different wavelengths (red and blue light) pass through the slits, no clear interference pattern arises. Each has a different wavelength, thus they lack the necessary coherence.

Light Wavelength

Wavelength is the distance between successive peaks of a wave. In terms of light, different colors correspond to different wavelengths, with red light having a longer wavelength than blue light.

Wavelength directly affects interference in several ways:

• It determines the spacing between the bright and dark bands in the interference pattern.
• Light of different wavelengths (like red and blue) results in patterns that do not overlap or match consistently unless other parameters are adjusted to create coherence.

In Young's double slit experiment, the filters cause each slit to emit light of a specific wavelength. When light of uniform wavelength passes through both slits, it’s easier for interference patterns to form because each wave maintains a consistent path difference. But if two different wavelengths are used simultaneously, the combination results in mixed but incoherent signals, which are not suitable for forming a standard interference pattern.