1. Goal: maximum transmission
   For a thin film coating, maximum transmission means minimum reflection.

2. Given

• Refractive index of film: $n_f = 2.0$
• Refractive index of glass slab: $n_g = 1.45$
• Wavelength of green light in air: $\lambda = 550\,\text{nm}$
• Incidence is nearly normal.

3. Phase changes at reflections Light is incident from air $(n\approx 1)$ onto film $(n=2.0)$ and then onto glass $(n=1.45)$.

• At air $\to$ film: reflection occurs from lower to higher refractive index, so reflected ray gets a phase shift of $\pi$.
• At film $\to$ glass: reflection occurs from higher to lower refractive index, so no phase shift.

Thus, the two reflected rays already differ by a phase of $\pi$ due to reflection.

4. Condition for maximum transmission To make reflection minimum, the two reflected rays must interfere destructively.

Because there is already a phase difference of $\pi$ at reflection, destructive interference occurs when the phase due to path difference is an integer multiple of $2\pi$:

$2 n_f t = m\lambda$

For the minimum non-zero thickness, take $m=1$:

$2 n_f t = \lambda$

$t = \frac{\lambda}{2 n_f}$

5. Substitute values

$t = \frac{550}{2\times 2.0}\,\text{nm} = \frac{550}{4}\,\text{nm} = 137.5\,\text{nm}$

6. Check options

• A: $68.7\,\text{nm}$
• B: $137.5\,\text{nm}$ ✅
• C: $94.8\,\text{nm}$
• D: $275\,\text{nm}$

Therefore, the correct option is B.