Find the thickness in a CD that has a plastic transparent layer with index of refraction 1.60 and is designed for use in a CD player using a layer of wavelength 780 nm in air?

To find the thickness of the plastic transparent layer in the CD, we can use the formula for the thickness of a thin film:

t = (m + 1/2) * λ / (2 * n)

Where:
t = thickness of the layer
m = order of the interference (for constructive interference, m = 0)
λ = wavelength of light in air (780 nm)
n = index of refraction of the plastic layer (1.60)

Plugging in the values:

t = (0 + 1/2) * 780 nm / (2 * 1.60)
t = 390 nm / 3.20
t = 121.875 nm

Therefore, the thickness of the plastic transparent layer in the CD is approximately 121.875 nm.

The thickness of the plastic transparent layer can be calculated using the formula:

$$t = \frac{\lambda}{4n}$$

where:

- t is the thickness of the layer
- λ is the wavelength of the light in air
- n is the index of refraction of the layer

In this case, the wavelength of the light in air is 780 nm and the index of refraction of the layer is 1.60. Substituting these values into the formula, we get:

$$t = \frac{780 \ nm}{4(1.60)} = 122.5 \ nm$$

Therefore, the thickness of the plastic transparent layer is 122.5 nm.