AIIMS 2006 Physics Total Internal Reflection Assertion Reason Question

To understand the question, we need to analyze both the assertion and the reason in the context of optical fibers and the principle of total internal reflection.

Assertion:

In optical fibre, the diameter of the core is kept small.

This assertion is true. The core of an optical fiber, which is the central part where light travels, is designed to have a small diameter (typically in the range of a few micrometers) to facilitate the guiding of light through the fiber by total internal reflection. A smaller diameter helps to confine the light within the core more effectively.

Reason:

This smaller diameter of the core ensures that the fibre should have incident angle more than the critical angle required for total internal reflection.

This reason is also true. The phenomenon of total internal reflection occurs when the angle of incidence exceeds the critical angle. For an optical fiber to work effectively, light must strike the core-cladding interface at an angle greater than this critical angle. A smaller core diameter allows for a greater variety of angles of incidence and helps to maintain the required conditions for total internal reflection.

The Critical Angle:

The critical angle ($\theta_c$) can be calculated using Snell's Law, which states:

$n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$

where:

• $n_1$ is the refractive index of the core,
• $n_2$ is the refractive index of the cladding,
• $\theta_1$ is the angle of incidence in the core,
• $\theta_2$ is the angle of refraction in the cladding.

Using the definition of the critical angle, where $\theta_2$ is $90^\circ$ (which means $\sin(\theta_2) = 1$), we derive the critical angle as:

$\sin(\theta_c) = \frac{n_2}{n_1}$

This indicates that for total internal reflection to take place, the angle of incidence must be greater than this critical angle.

Conclusion:

Since both the assertion and reason are true, and the reason correctly explains the assertion, the correct answer is:

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 is indeed a valid explanation for why the core's diameter is kept small.
• Option C: Assertion is true but Reason is false. This is incorrect because both statements are true.
• Option D: Both Assertion and Reason are false. This is incorrect as both statements are true.

Summary:

In summary, the small diameter of the core in optical fibers allows light to be guided by total internal reflection, and the requirement for light to strike at angles greater than the critical angle is essential for this phenomenon to occur. Thus, the assertion and reason both support one another logically.