The minimum value of the index of refraction (n) of the glass sheet that produces the effect of the first gap at 564 nm is approximately 4.26.
To calculate the minimum value of the index of refraction (n) of the glass sheet, we can use the formula for the gap in the visible spectrum:
n * λ = 2 * t * m
Where:
- n is the index of refraction of the glass
- λ is the wavelength of light in the gap
- t is the thickness of the glass sheet
- m is an integer representing the order of the gap (e.g., m = 1 for the first gap, m = 2 for the second gap, and so on)
We are given two gaps in the visible spectrum at 564 nm and 635.00 nm. Let's consider the first gap with a wavelength of 564 nm and set m = 1:
n * 564 nm = 2 * 1.20 μm * 1
To simplify the calculation, let's convert the thickness of the glass sheet from micrometers to nanometers:
t = 1.20 μm = 1200 nm
Rearranging the equation to solve for n:
n = (2 * 1200 nm) / 564 nm
Calculating the value of n:
n ≈ 4.26