Question

What is the total optical path length of two media in contact with thicknesses of \(d\) and \(\frac{d}{4}\) and refractive indices of \(n_{1}\) and \(n_{2}\), respectively?

• A. \(\frac{d(n_{1}+4n_{2})}{4}\)
• B. \(\frac{d(4n_{1}+n_{2})}{4}\)
• C. \(\frac{d(n_{1}+n_{2})}{4}\)
• D. \(d(4n_{1}+n_{2})\)

Hint:

Optical path in a medium is refractive index times geometrical thickness. Add the paths for both media.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
The optical path length in a medium is the refractive index multiplied by the geometrical thickness.

Step 2: Each medium
First medium: \(n_{1}d\). Second medium: \(n_{2}\cdot\dfrac{d}{4}\).

Step 3: Total
\(n_{1}d+\dfrac{n_{2}d}{4}=\dfrac{d(4n_{1}+n_{2})}{4}\)

Final Answer:
The total optical path is d times 4 n1 plus n2, all divided by 4. \[ \boxed{\text{(B) }\dfrac{d(4n_{1}+n_{2})}{4}} \]