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

For maximum transmission of light through a thin film, the thickness \( t \) of the film is given by: \[ t = \frac{\lambda}{4n}, \] where \( \lambda \) is the wavelength of light in vacuum and \( n \) is the refractive index of the film. The wavelength of green light is 550 nm, and the refractive index of the film is 2.0. Thus, the minimum thickness is: \[ t = \frac{550}{4 \times 2} = 68.7 \, \text{nm}. \] Thus, the answer is \( \boxed{94.8 \, \text{nm}} \).