A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1

Описание: A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength 550 nm. [Assume that the light is incident nearly perpendicular to the glass
surface.]
(1) 94.8 nm (2) 68.7 nm
(3) 137.5 nm (4) 275 nm

🌟 Understanding Thin Film Interference for Maximum Transmission 🌟

When light passes through a thin film, interference occurs due to reflections from the top and bottom surfaces of the film. This interference can be constructive (leading to maximum transmission) or destructive (leading to minimum transmission), depending on the optical path difference between the reflected waves.

In this case, a transparent film of refractive index 2.0 is coated on a glass slab with a refractive index of 1.45**. The goal is to determine the **minimum thickness of the transparent film that results in maximum transmission for **green light with a wavelength of 550 nm**. 🌈🔬

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🔹 Concept of Thin Film Interference

Interference in thin films occurs due to the reflection of light from both the upper surface (air-film interface) and the lower surface (film-glass interface). The two reflected rays interfere either constructively or **destructively**, depending on the optical path difference between them.

Phase Change Considerations:
• When light moves from a lower refractive index medium to a higher refractive index medium**, a **phase change of 180° (or π radians) occurs upon reflection.
• When light moves from a higher refractive index medium to a lower refractive index medium**, **no phase change occurs.

In this case:
✔️ Reflection at the air-to-film interface (n = 1 → n = 2) induces a phase shift of π (180°).
✔️ Reflection at the film-to-glass interface (n = 2 → n = 1.45) does not induce a phase shift because light moves from a higher to a lower refractive index.

Condition for Maximum Transmission (Destructive Interference in Reflection)
For maximum transmission**, we need to minimize reflection, which occurs when **destructive interference happens in the reflected light.

For destructive interference**, the optical path difference (OPD) should be equal to an **odd multiple of λ/2 inside the film:
🔥 Key Takeaways for JEE & NEET Aspirants
✔️ Thin Film Interference occurs due to reflections from the top and bottom surfaces of a film.
✔️ Phase change of 180° happens when light reflects from a **lower to a higher refractive index medium**.
✔️ Maximum transmission occurs when destructive interference minimizes the reflected light.
✔️ The minimum thickness for maximum transmission is **t = λ / 4n**.
✔️ Understanding this concept is crucial for wave optics problems in **JEE Mains & NEET**! 🚀🔬