1) PLEASE BE CLEAR ON YOUR RESPONSE AND ACCURACY, THANKS. **Educational Content on Wave Interference**In the figure, we analyze two waves of light in air, each initially in phase and having a wavelength of 428 nm. One wave travels through a glass layer with an index of refraction \( n_1 = 1.55 \) and thickness \( L \). The other wave travels through a plastic layer with an index of refraction \( n_2 = 1.20 \), also of thickness \( L \).### Key Points1. **Phase Difference:** - We seek the smallest value of \( L \), in meters, such that the phase difference between the two waves is 5.91 radians.2. **Interference Type:** - When both waves arrive at a common point with the same amplitude, we need to determine whether their interference is: - Fully constructive - Fully destructive - Intermediate but closer to fully constructive - Intermediate but closer to fully destructive### Diagram Explanation- The diagram depicts two horizontal arrows representing light waves traveling through different layers.- Two rectangular sections are colored distinctly (yellow for \( n_1 \) and green for \( n_2 \)), illustrating the glass and plastic layers.- Both layers have the same thickness, \( L \).### Questions:- **(a)** Calculate the smallest \( L \) for the specified phase difference.- **(b)** Determine the nature of the interference between the waves at the point where they meet.The understanding of how light waves travel through different media and interfere with each other is crucial in optics and various practical applications, such as designing lenses and other optical devices.

The two waves of light are initially travelling in phase. Their wavelength is 428 nm Let λ=428 nmλ=428×10-9 m Both of these light waves are then passed through two different mediums, one goes through glass, with a refractive index of 1.55, while the other goes through a plastic layer, with refractive index 1.2. Both having the same thickness As these light waves travel through these denser mediums, their velocities in both these mediums will change, and will depend on the index of refraction. The speed of light travelling in a denser medium is different from when it travels in vacuum or air. As a result, the speeds of both the light waves moving through the two mediums will change, and will be different, due to their different refractive indices. Thus, when the two light waves emerge out of their respective mediums, they will have a path difference between them, since one of the light waves travels faster than the other. When inside their media, the optical path length traveled by both the light waves is d1=n1Ld2=n2L This optical path traveled by both the waves will be different, due to the different indexes of refraction, and thus, the path difference between the two waves as they come out of their media will be ∆d=d1-d2∆d=n1L-n2L∆d=1.55-1.2L∆d=0.35L When the waves come out of their media, there is a phase difference of 5.91 radians between the two. Phase difference and path difference between two waves are related as ϕ=2πλ∆d∆d=λ2πϕ0.35L=428×10-92π×5.91L=4.026×10-70.35L=1.15×10-6 m This is required value for the thickness L Interference of two or more waves can be either constructive or destructive, depending on their path difference. If the path difference between the two waves is an integral multiple of their wavelength, then the corresponding interference will be constructive, and if the path difference between the two waves is a half integral multiple of their wavelength, then the interference will be destructive The path difference between these two waves is ∆d=0.35L∆d=0.35×1.15×10-6∆d=4.0258×10-7∆d=402.58×10-9 m∆d=402.58 nm And the wavelength of the light waves is λ=428 nm The condition for constructive interference is ∆d=nλn=∆dλn=402.58428n=0.94 Since this number is not an integral number, the waves will not interfere constructively.Condition for destructive interference, ∆d=n+12λn+12=∆dλn+12=0.94n=0.94-12n=0.44 Thus, again since n is not an integral value, so the waves also do not construct destructively Thus, the waves have an intermediate interference, consisting of both, a constructive and a destructive part. But since the value of n for constructive interference is much closer to being an integral value, so the waves are closer to a fully constructive interferenceAnswers: Length, L=1.15 x 10-6 m Intermediate interference, closer to being fully constructive

Answered: In the figure, assume two waves of…