A sheet of plastic (n = 1.56) covers one slit of a double slit (see the drawing). When the double slit is illuminated by monochromatic light (vacuum = 568 nm), the center of the screen appears dark rather than bright. What is the minimum thickness of the plastic?
all that is changed is the light is slowed in the plastic, so that there is a "distance" to be added to the plastic path (disance= deltaTimedelay*speedlight).
so at the center, the two beams are 180 deg out of phase, so it means 2*"distance" above= wavlength light.
what is time delay? well, it has to be
(n-1)thicknessplastic
2*speedlight*(n-1)thicknessplastic)=wavelength
chck my thinking.
To find the minimum thickness of the plastic sheet, we need to understand the phenomenon of interference and how light interacts with the sheet.
When light passes through a material with a different refractive index, such as the plastic sheet in this case, it undergoes both reflection and refraction. The phase shift introduced by the reflection and refraction at the surface of the material affects the interference pattern formed by the double slit.
In this scenario, since the center of the screen appears dark rather than bright, it suggests that the phase shift due to the reflection and refraction at the surface of the plastic sheet is causing destructive interference.
To find the minimum thickness, we can use the equation for the phase shift caused by refraction at the boundary between mediums:
Δφ = (2π/λ) * d * (n - 1)
where Δφ is the phase difference, λ is the wavelength of light in vacuum, d is the thickness of the plastic sheet, and n is the refractive index of the plastic.
In this case, we want destructive interference at the center, which corresponds to a phase shift of π radians (180 degrees). Therefore, we can set Δφ equal to π and solve for d:
π = (2π/λ) * d * (n - 1)
Simplifying the equation, we have:
d = λ / (2 * (n - 1))
Substituting the given values: λ = 568 nm (or 568 × 10^-9 m) and n = 1.56, we can calculate the minimum thickness of the plastic sheet.
d = (568 × 10^-9 m) / [2 * (1.56 - 1)]
By evaluating the above expression, we find that the minimum thickness of the plastic sheet is approximately 2.37 × 10^-7 meters or 237 nm.