Part (a)
Correct Answer: The ratio of the speed of light in air (or vacuum) to the speed of light in the soap film.
The refractive index ($n$) is a dimensionless measure that describes how fast light travels through a material. It is formally defined as the ratio of the speed of light in a vacuum (approximated as the speed of light in air) to the speed of light in the specified medium: $n = \frac{c}{v}$.
Part (b)(i)
Correct Answer: $i = 60^{\circ}$, $1.28 = \frac{\sin 60^{\circ}}{\sin r}$, $r = 42.6^{\circ} \approx 43^{\circ}$
First, find the angle of incidence ($i$), which is measured from the normal. Since the ray makes a $30^{\circ}$ angle with the boundary, $i = 90^{\circ} – 30^{\circ} = 60^{\circ}$. Applying Snell’s Law, $n = \frac{\sin i}{\sin r}$, we rearrange to find $\sin r = \frac{\sin 60^{\circ}}{1.28}$. Calculating this gives $r \approx 42.6^{\circ}$, which rounds to $43^{\circ}$.
Part (b)(ii)
Correct Answer: A normal drawn at the incidence point; a refracted ray drawn bending towards the normal with the angle $r$ labeled.
Draw a dashed normal line perpendicular to the surface. The refracted ray should be drawn inside the film, bending toward the normal (since $r < i$).
Part (c)(i)
Correct Answer: Light of a single frequency.
Monochromatic light consists of waves with a single frequency (or wavelength), resulting in a single pure color.
Part (c)(ii)
Correct Answer: $4.4 \times 10^{14}\text{ Hz}$
Using $v = f\lambda$, where $v = 3.0 \times 10^8\text{ m/s}$ and $\lambda = 680 \times 10^{-9}\text{ m}$. Rearranging for frequency: $f = \frac{v}{\lambda} = \frac{3.0 \times 10^8}{680 \times 10^{-9}} \approx 4.4 \times 10^{14}\text{ Hz}$.
