As light travels from air into the water through the oil film, (Choose one)?

"Consider a thin, transparent film with thickness t and index of refraction n coated onto a piece of a given material. When a light wave of wavelength lambda approaches the film, although most of the light is transmitted into the film, a small portion is reflected off the first (air–film) boundary and another portion of the light that continues into the film is reflected off the second (film–material) boundary. The two reflected waves, which have exactly the same frequency, travel back out into the air, where they overlap and interfere. The way they interfere depends on their effective path-length difference.

Problem: A very thin oil film (noil=1.25) floats on water (nwater=1.33). What is the thinnest film that produces a strong reflection for green light with a wavelength of 500 nm?

PART A: As light travels from air into the water through the oil film, (Choose one)

a. both of the reflected rays undergo a phase change

b. neither of the reflected rays undergo a phase change

c. only one of the reflected rays undergo a phase change.

PART B: Which of the following equations should be used to find the minimum thickness t of the oil film that satisfies the conditions of the problem? Let lambda be the wavelength of light in air and n the index of refraction of the thin film.

2t=m\frac{\lambda}{n}\quad (m=0, 1, 2, ...) for constructive interference.

2t=\left( m+\frac{1}{2}\right) \frac{\lambda}{n}\quad (m=0, 1, 2, ...) for destructive interference.

2t=\left( m+\frac{_1}{^2}\right)\frac{\lambda}{n}\quad (m=0, 1, 2, ...) for constructive interference.

2t=m\frac{\lambda}{n}\quad (m=0, 1, 2, ...) for destructive interference.

PART C:

What is the minimum thickness t of the film that produces a strong reflection for green light with a wavelength of 500 \rm nm?

t= ______________ nm ?"