Question

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?

• A. 68.7 nm
• B. 275 nm
• C. 137.5 nm
• D. 94.8 nm

Hint:

The minimum thickness for maximum transmission in a thin film is given by \( t = \frac{\lambda}{4n} \), where \( n \) is the refractive index.

Answer 1

The Correct Option is A

To solve this problem, we need to consider the condition for constructive interference in thin films. For maximum transmission through the film, we require that the phase change due to the path difference between the reflected waves should result in constructive interference.

The condition for constructive interference in a thin film is given by:

2n_ft = (m + 0.5)λ₀,

where:

• n_f is the refractive index of the film, which is 2.0 in this case.
• t is the thickness of the film.
• λ₀ is the wavelength of light in vacuum, 550 nm for green light.
• m is the order of interference, and for minimum thickness, we take m = 0.

Substituting the values, we have:

2 × 2.0 × t = (0 + 0.5) × 550 nm

4t = 275 nm

Solving for t gives:

t = 275 nm / 4

t = 68.75 nm

Thus, the minimum thickness of the transparent film required for maximum transmission of green light is 68.75 nm. This closely matches the provided option 68.7 nm.