Waves

Define the Critical Angle

The angle of incidence, from a material of higher refractive index into a material of lower refractive index, that causes the angle of refraction to be 90 degrees / the emergent ray to refract along the boundary

In Reality, when will TIR occur? Why does this differ from the definition?

Once the angle of incidence = the critical angle

In reality, the emergent ray cannot travel along a line

True of False? The amplitude of both progressive waves must be the same / similar to form a stationary wave. Why?

True

Amplitudes must be same / similar to cause total destruction at nodes

What must be true for the intensity of the fringes to remain constant in Young’s double slit interference pattern?

aperture width = wavelength

(ensures angle for first minima is large, so single slit minima never form)

Do distinct minima form when using white light in:

a) Single slit diffraction

b) Young’s double slit

c) Diffraction gratings

a) No

b) No

c) Yes

Describe the diffraction pattern when using white light with a diffraction grating.

The central maxima is white + most intense.

Moving outwards, we get the individual wavelength maxima at different angles (e.g. a blue dot, a gap, a green dot, etc).

Looking at it as an overview, we get white dot in middle, then a repeating pattern either side of blue to red then blue to red, with minima between every order (though with distance, some orders may begin to overlap.)

What are the uses of diffraction gratings?

X-ray crystallography (determines spacing between atoms)

Observing light from distant stars / galaxies (used to produce absorption spectra)

Identifying elements : in stars, in unknown samples) - (by either comparing emission / absorption spectra or measuring the angle to find the wavelength)

Which formula relies on small angle approximations?

w = lambda D / s

In the Young’s double slit fringe width approximation formula, what must be true to ensure the small angle approximation can be used?

D » s and D » w

Note that D will be much larger than lambda but that is more indirect

What is the approximate refractive index of air?

1