Find the pit depth in a CD that has a plastic transparent layer with index of refraction 1.60 and designed for use In a CD player using a layer of wavelength 7.8×10^2 nm in air?

To find the pit depth in a CD, we can use the formula for the depth of a pit in a CD:

depth = (wavelength / (4 * (n - 1))) * (1 - sqrt(1 - (1 / n^2)))

where:
- wavelength = 7.8×10^2 nm
- n = index of refraction of the plastic layer = 1.60

Plugging in the values:

depth = (7.8×10^2 nm / (4 * (1.60 - 1))) * (1 - sqrt(1 - (1 / 1.60^2)))
depth = (7.8×10^2 nm / (4 * 0.60)) * (1 - sqrt(1 - (1 / 2.56)))
depth = (7.8×10^2 nm / 2.4) * (1 - sqrt(1 - 0.390625))
depth = 325 nm * (1 - sqrt(0.609375))
depth = 325 nm * (1 - 0.780)
depth = 325 nm * 0.220
depth = 71.5 nm

Therefore, the pit depth in the CD is approximately 71.5 nm.

The pit depth can be calculated using the following formula:

$$d = \frac{\lambda}{2n}$$

Where:

- d is the pit depth
- λ is the wavelength of the light in air
- n is the index of refraction of the plastic transparent layer

Substituting the given values into the formula, we get:

$$d = \frac{7.8 \times 10^{-7} \text{ m}}{2 \times 1.60} = 2.44 \times 10^{-7} \text{ m}$$

Therefore, the pit depth is 244 nm.