A puddle of water (n = 1.33) is covered with a very thin layer of light oil (n = 1.20). What is the minimum thickness the oil in the region that does not reflect light with a wavelength of 550 nm?

To determine the minimum thickness of the oil in the region that does not reflect light with a wavelength of 550 nm, we can use the concept of thin film interference.

The condition for destructive interference in thin films is given by the equation:

2nt = (m + 1/2)λ

Where:
- n is the index of refraction of the medium (in this case, the oil)
- t is the thickness of the oil layer
- m is an integer representing the order of the interference
- λ is the wavelength of light

In this case, we want to find the minimum thickness of the oil that does not reflect light with a wavelength of 550 nm. So, we can rearrange the equation as follows:

t = ((m + 1/2)λ) / (2n)

Since we're interested in the minimum thickness, we can use the first-order destructive interference (m = 0). Substituting the known values into the equation:

t = ((0 + 1/2) × 550 nm) / (2 × 1.20)

Simplifying the equation:

t = (1/2 × 550 nm) / 2.40

t = 275 nm / 2.40

t ≈ 114.58 nm

Therefore, the minimum thickness of the oil in the region that does not reflect light with a wavelength of 550 nm is approximately 114.58 nm.

To find the minimum thickness of the oil in the region that does not reflect light with a wavelength of 550 nm, we need to use the concept of thin film interference.

Thin film interference occurs when light waves reflect from both the upper and lower surfaces of a thin film, creating constructive and destructive interference patterns. At certain thicknesses, the reflected waves interfere destructively, resulting in no reflected light for a specific wavelength.

Here are the steps to solve the problem:

Step 1: Determine the conditions for destructive interference. Destructive interference occurs when the path difference between the upper and lower reflected waves is equal to half a wavelength (λ/2).

Step 2: Calculate the path difference. The path difference can be calculated using the formula: Path difference = 2 * thickness * refractive index.

Step 3: Set up the equation. Set the path difference equal to λ/2 and rearrange the equation to solve for the thickness of the oil: Thickness = (λ/2) / (2 * refractive index).

Step 4: Substitute the values. Substitute the given values into the equation: λ = 550 nm (converted to meters), refractive index of water (n₁) = 1.33, and refractive index of oil (n₂) = 1.20.

Step 5: Calculate the minimum thickness. Plug in the values and evaluate the equation to find the minimum thickness of the oil in the region that does not reflect light with a wavelength of 550 nm.

Let's solve the equation:

Thickness = (λ/2) / (2 * refractive index)

Given:
λ = 550 nm = 550 * 10^(-9) m
Refractive index of water (n₁) = 1.33
Refractive index of oil (n₂) = 1.20

Substituting the values:

Thickness = (550 * 10^(-9) m / 2) / (2 * 1.20)

Now, calculate the minimum thickness:

Thickness ≈ 0.229 * 10^(-6) m or 2.29 * 10^(-7) m

Therefore, the minimum thickness of the oil in the region that does not reflect light with a wavelength of 550 nm is approximately 2.29 * 10^(-7) meters.

A puddle holds 150 g of water. If 0.50 g of water evaporates from the surface, what is the approximate temperature change of the remaining water? (Lv = 540 cal/g)