AIIMS 2006 Physics Diffraction Assertion Reason Question

To analyze the given question, we need to delve into the concepts of diffraction gratings and the wavelengths of X-rays.

Explanation of the Assertion and Reason

Assertion: Standard optical diffraction gratings cannot be used for discriminating between different X-ray wavelengths.

Reason: The grating spacing is not of the order of X-ray wavelengths.

1. Understanding Diffraction Gratings: A diffraction grating consists of a series of closely spaced slits or grooves. It disperses light into its component wavelengths based on the principle of interference. The formula for the angle of diffraction, $\theta$, for constructive interference is given by:

   $$d \sin \theta = n \lambda$$

   where:

   • $d$ is the grating spacing (distance between adjacent slits),
   • $\theta$ is the angle of diffraction,
   • $n$ is the order of the diffraction,
   • $\lambda$ is the wavelength of the light (or radiation).

2. Wavelengths of X-rays: X-rays typically have wavelengths on the order of $0.01$ nm to $10$ nm (or $10^{-11}$ m to $10^{-8}$ m).

3. Grating Spacing Comparison: Standard optical diffraction gratings are designed for visible light, which has wavelengths around $400$ nm to $700$ nm (or $4 \times 10^{-7}$ m to $7 \times 10^{-7}$ m). The grating spacing for optical gratings is usually on the order of micrometers ($10^{-6}$ m). Therefore, the grating spacing for standard optical gratings is significantly larger than the wavelengths of X-rays.

Conclusion for the Correct Answer

Since the grating spacing ($d$) of standard optical gratings is not suitable for the much smaller X-ray wavelengths ($\lambda$), it leads to the conclusion that standard optical diffraction gratings cannot effectively discriminate between different X-ray wavelengths. Thus, both the assertion and the reason are true, and the reason correctly explains why the assertion holds.

Correct Answer: A) Both Assertion and Reason are true and Reason is the correct explanation of Assertion.

Clarification of Other Options

• Option B: Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion. This is incorrect because the reason provided directly supports the assertion.

• Option C: Assertion is true but Reason is false. This is incorrect because the reason is indeed true; the grating spacing does not accommodate X-ray wavelengths.

• Option D: Both Assertion and Reason are false. This option is incorrect as both the assertion and the reason are true.

Summary

In summary, the conclusion that standard optical diffraction gratings cannot discriminate X-ray wavelengths is supported by the fact that their grating spacing is not of the order of X-ray wavelengths, making option A the correct choice. This understanding of diffraction and wavelength scales is critical in optics, particularly when differentiating between types of electromagnetic radiation.