Optical Path Length – Rankers Physics
Topic: Ray Optics
Subtopic: Refraction by Plane Surfaces

Optical Path Length


Assertion (A): Optical path length is always greater than or equal to geometrical path length.
Reason (R): Light travels with speed of \(3 \times 10^8 \text{ m/s}\) in vacuum.
 
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:

Optical path length \(OPL = \mu \times L\), where \(\mu\) is the refractive index and \(L\) is the geometrical path length. Since \(\mu \ge 1\) for all transparent media, \(OPL \ge L\). So (A) is true. Light travels at \(3 \times 10^8 \text{ m/s}\) in vacuum. So (R) is true. However, (R) does not explain (A); (A) is explained by the definition of refractive index (\(\mu = c/v\)) which implies \(\mu \ge 1\) because \(v \le c\). Thus, (R) is true but not the correct explanation for (A).

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