Question

A teacher places a fluid substance, with a refractive index of 1.69, between two horizontal panes of flat glass (each of which has n=1.55). He then illuminates the assembly from above with monochromatic light (A=340 nm). What is the minimum thickness (in nm) that the liquid layer must have, if the light is to be strongly reflected back toward its source? nm

Answer 1

The minimum thickness of the liquid layer for strong reflection of light is achieved when the round-trip optical path difference between two waves equals an integer multiple of wavelength in the liquid. Considering the minimum thickness, the integer multiple is taken as one. Therefore, the minimum thickness required for strong reflection is 100.59 nm.

Step-by-step explanation:

The minimum thickness of the liquid layer that will reflect the light back to its source is governed by the idea of constructive interference in the context of thin films. Based on the principles of wave interference, when the path difference between two waves is equal to an integer multiple of the wavelength, the waves constructively interfere to create a larger amplitude wave.

In this case with a fluid substance (with a refractive index, n of 1.69), placed between two horizontal panes of flat glass (each with a refractive index, n of 1.55), the condition for strong reflection will occur when the round-trip optical path difference (2nd, where d is the thickness of the liquid layer) equals mλ in the liquid, 'm' being an integer.

Considering the minimum thickness, we should use m=1. Since the wavelength in the fluid is less than in vacuum due to the refractive index, λ'= λ/n = 340 nm / 1.69 ≈ 201.18 nm. Hence, the minimum thickness (d) that satisfies the condition is λ'/2 = 201.18 nm / 2 = 100.59 nm.

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