Question

A 3.7 cm -thick layer of oil is sandwiched between a 1.2 cm -thick sheet of glass and a 2.7 cm -thick sheet of polystyrene plastic.How long (in ns) does it take light incident perpendicular to the glass to pass through this 7.6 cm -thick sandwich?

Answer 1

Answer 2

The speed of light in a vacuum is approximately 3 x 10^8 m/s. However, the speed of light in a medium, such as glass or oil, is slower than in a vacuum and is characterized by the refractive index of the medium.

We can use Snell's Law to calculate the angle of refraction of the light as it passes through each layer, and then use the thickness and refractive index of each layer to calculate the time taken for the light to pass through the sandwich.

Let's start by calculating the refractive index of each layer. The refractive index of glass is approximately 1.5, and the refractive index of polystyrene is approximately 1.6. The refractive index of oil varies depending on the type of oil, but for this problem, we will assume it is approximately 1.45.

Next, we can use Snell's Law to calculate the angle of refraction of the light as it passes through each layer. Snell's Law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media. Since the angle of incidence is 0° (the light is incident perpendicular to the glass), the angle of refraction is also 0° for the glass-oil interface and the oil-polystyrene interface.

Therefore, the light passes straight through the glass layer, and the only time delay comes from the oil and polystyrene layers. The time delay is given by:

time delay = thickness / (speed of light in medium)

For the oil layer, the thickness is 3.7 cm and the speed of light in oil is:

speed of light in oil = speed of light in vacuum / refractive index of oil speed of light in oil = (3 x 10^8 m/s) / 1.45 speed of light in oil = 2.07 x 10^8 m/s

Therefore, the time delay for the oil layer is:

time delay for oil = 3.7 cm / (2.07 x 10^8 m/s) = 1.79 x 10^-8 s

For the polystyrene layer, the thickness is 2.7 cm and the speed of light in polystyrene is:

speed of light in polystyrene = speed of light in vacuum / refractive index of polystyrene speed of light in polystyrene = (3 x 10^8 m/s) / 1.6 speed of light in polystyrene = 1.875 x 10^8 m/s

Therefore, the time delay for the polystyrene layer is:

time delay for polystyrene = 2.7 cm / (1.875 x 10^8 m/s) = 1.44 x 10^-8 s

The total time delay is the sum of the time delays for the oil and polystyrene layers:

total time delay = time delay for oil + time delay for polystyrene total time delay = 1.79 x 10^-8 s + 1.44 x 10^-8 s total time delay = 3.23 x 10^-8 s

Therefore, the time taken for the light to pass through the 7.6 cm-thick sandwich is:

time taken = 3.23 x 10^-8 s + time taken for glass layer time taken = 3.23 x 10^-8 s + (1.2 cm / (3 x 10^8 m/s)) time taken = 3.23 x