Optical Density and Refractive Index in Air – Rankers Physics

Total Internal Reflection: Practice Problem & Solution

Assertion (A): On hot summer days, optical density of different layer of air increases with height from ground. Reason (R): Refractive index of air increases with its density.  
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution Explained:

To solve this problem, we apply the core principles of Total Internal Reflection. Understanding the underlying formula is key to arriving at the correct answer below:

On hot summer days, air near the ground is hotter and less dense. As height increases, air becomes cooler and denser. Since refractive index (and thus optical density) increases with density, the optical density of air layers increases with height. Therefore, both assertion and reason are true, and the reason explains the assertion.

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