Question

A scientist notes a pretty oil slick on the surface of a body of water. She aims her spectrometer at a spot on the oil slick to measure the wavelength that is being most strongly reflected. The oil index is 1.2, and she finds maximum reflection at a wavelength of 750 nm. what is the minimum thickness t of the oil stick at the spot?

Answer 1

The minimum thickness of the oil slick at the spot where the wavelength of 750 nm is most strongly reflected is calculated using the formula for thin film interference. Considering the given index of refraction (n = 1.2), the thickness is found to be 312.5 nm.

Step-by-step explanation:

To calculate the minimum thickness of the oil slick at the spot where a wavelength of 750 nm is most strongly reflected, we utilize the concept of thin film interference. In this scenario, constructive interference occurs, and we apply the formula for the minimum thickness of the thin film:

t = (m + ½) × (λ/n)

Where t is the thickness of the oil film, m is the order number (which is zero for the first minimum thickness), λ is the wavelength of the light in a vacuum, and n is the index of refraction of the oil.

Given that the index of refraction of the oil (n) is 1.2 and the wavelength (λ) is 750 nm, we calculate the following:

t = (0 + ½) × (750 nm / 1.2) = ½ × 625 nm = 312.5 nm

Therefore, the minimum thickness of the oil slick at the spot is 312.5 nm.

Answer 2

Answer: t=156.25 nm

Step-by-step explanation:

For finding the minimum thickness t of the oil stick when maximum reflection occurs,

It is given by formula

2 n t = (m +
`(1)/(2)`) λ

Here we need to find that minimum thickness so put m= 0,

Also, λ= 750 nm

n= 1.2

So putting the values we get

2 *(1.2)* t = (0 +
`(1)/(2)`) * 750 nm

Or t=
`(1)/(2*2*1.2) * 750`

t= 156.25 nm which is the minimum thickness t of the oil stick at the spot