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.]

Step 1: Condition for Maximum Transmission (Minimum Reflection)

For a thin film on a denser medium, the condition for destructive interference (so that light does not reflect and is mostly transmitted) is:

$$2 t n = m \lambda$$

For minimum thickness, we take m = 1:

$$2 t n = \lambda$$

Step 2: Given Data

Refractive index of the film: $n = 2.0$

Refractive index of glass: $n_{\text{glass}} = 1.45$ (not needed for calculation)

Wavelength of green light in air: $\lambda = 550$nm

Step 3: Calculate the Minimum Thickness

Rearranging the equation:

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

Substituting values:

$$t = \frac{550}{2 \times 2.0}$$

 $$t = \frac{550}{4} = 137.5 \text{ nm}$$