When you look through a 3.7 mm thick window comprised of a material whose refractive index is 1.59, by what time interval is the light you see delayed by having to go through glass instead of air?
To calculate the time delay experienced by light while passing through a medium, you can use the formula:
Δt = (d * n) / c
Where:
Δt is the time delay
d is the thickness of the medium
n is the refractive index of the medium
c is the speed of light in a vacuum (approximately 3.00 × 10^8 meters per second)
In this case, the thickness of the window is given as 3.7 mm, and the refractive index is 1.59. We need to convert the thickness from millimeters to meters to maintain consistent units. Since 1 mm = 0.001 m, the thickness of the window is 3.7 mm * 0.001 m/mm = 0.0037 m.
Substituting the values into the formula:
Δt = (0.0037 m * 1.59) / (3.00 × 10^8 m/s)
Now, let's calculate the time delay:
Δt = (0.0037 * 1.59) / (3.00 × 10^8)
= 0.005913 / 3.00 × 10^8
= 1.97 × 10^-11 seconds
Therefore, the light is delayed by approximately 1.97 × 10^-11 seconds when passing through the 3.7 mm thick window with a refractive index of 1.59.
To calculate the time delay experienced by light when it passes through a material, we can use the formula:
t = (d / c) * (n - 1)
Where:
t is the time delay,
d is the thickness of the material,
c is the speed of light in vacuum, and
n is the refractive index of the material.
Let's plug in the given values to calculate the time delay:
d = 3.7 mm = 0.0037 m (converting millimeters to meters)
n = 1.59 (refractive index of the material)
c = 299,792,458 m/s (speed of light)
t = (0.0037 / 299,792,458) * (1.59 - 1)
t ≈ (1.233 × 10^-11) * (0.59)
t ≈ 7.26 × 10^-12 s
Therefore, the light is delayed by approximately 7.26 picoseconds (ps) when passing through the 3.7 mm thick window comprised of a material with a refractive index of 1.59.