K A Tsokos Solutions for Chapter: Wave Phenomena (HL), Exercise 3: Test yourself

In a Young's two-slit experiment it is found that an $n^{th}$-order maximum for a wavelength of $680.0\mathrm{nm}$ coincides with the ${\left(n+1\right)}^{th}$ maximum of light of wavelength $510.0\mathrm{nm}$. Determine $n$.

Light is incident normally on two narrow parallel slits a distance of $1.00\mathrm{mm}$ apart. A screen is placed a distance of $1.2\mathrm{m}$ from the slits. The distance on the screen between the central maximum and the centre of the $n=4$ bright spot is measured to be $3.1\mathrm{mm}$.

a. Determine the wavelength of light.

Light is incident normally on two narrow parallel slits a distance of $1.00\mathrm{mm}$ apart. A screen is placed a distance of $1.2\mathrm{m}$ from the slits. The distance on the screen between the central maximum and the centre of the $n=4$ bright spot is measured to be $3.1\mathrm{mm}$.

b. This experiment is repeated in water (of refractive index $1.33$). Suggest how the distance of $3.1\mathrm{mm}$ would change, if at all.

The graph shows the intensity pattern from a two-slits interference experiment.

a. Determine the separation of the slits in terms of the wavelength of light used.

The graph shows the intensity pattern from a two-slits interference experiment.

b. Suggest how the pattern in the previous question change if the slit separation changes.

A piece of glass of index of refraction $1.50$ is coated with a thin layer of magnesium fluoride of the index of refraction $1.38$. It is illuminated with light of the wavelength of $680\mathrm{nm}$. Determine the minimum thickness of the coating that will result in no reflection.

A thin soap bubble of the index of refraction $1.33$ is viewed with the light of wavelength $550.0\mathrm{nm}$ and appears very bright. Predict a possible value of the thickness of the soap bubbles.

Describe how the graph you drew in a change when:

ii The number of slits stays at two but their separation decreases.