AIIMS 2007 Physics Interference Assertion Reason Question

To analyze the given assertion and reason, we need to delve into the principles of wave optics, specifically focusing on the interference of light.

Assertion Analysis:

Assertion: A white source of light during interference forms only white and black fringes.

This assertion is false. When white light (which contains multiple wavelengths corresponding to different colors) is used in an interference experiment, such as Young's double-slit experiment, the resulting pattern is not limited to just white and black fringes. Instead, it produces a spectrum of colors due to the superposition of light waves of different wavelengths. Each wavelength will produce its own set of fringes, leading to a colorful interference pattern rather than just black and white.

Reason Analysis:

Reason: Width of fringe is inversely proportional to the wavelength of the light used.

This reason is true. The fringe width $\beta$ in an interference pattern can be given by the formula:

$$\beta = \frac{\lambda D}{d}$$

where:

• $\beta$ is the fringe width,
• $\lambda$ is the wavelength of the light,
• $D$ is the distance from the slits to the screen,
• $d$ is the distance between the slits.

From this formula, we can see that as the wavelength $\lambda$ increases, the fringe width $\beta$ also increases. Conversely, if the wavelength decreases, the fringe width decreases, indicating that the fringe width is inversely proportional to the wavelength.

Conclusion:

Since the assertion is false and the reason is true, the correct answer is D) If both assertion and reason are false. However, this is incorrect as per the reasoning provided above. The assertion is false while the reason is true, making the correct conclusion that:

• Assertion is false.
• Reason is true.

Why Other Options Are Incorrect:

• Option A: This option would be correct if both the assertion and reason were true, which they are not.
• Option B: This option suggests both are true, which is incorrect since the assertion is false.
• Option C: This option claims the assertion is true but the reason is false. This is incorrect as the reason is indeed true.

In summary, the correct disposition is that the assertion is false (regarding the nature of the interference pattern formed by white light), while the reason is true (regarding the relationship between fringe width and wavelength).

Thus, the precise conclusion should be revised as: Assertion is false, Reason is true. However, based on the choices given, if we follow what is stated in the question, we would select option D, but with a caveat that it does not accurately reflect the truth of the reason.