iGCSE Physics (0625) 3.2.2 Refraction of light-Exam Style Questions- New Syllabus
▶️ Answer/Explanation
Detailed solution:
First, calculate the refractive index $n$ using Snell’s Law: $n = \frac{\sin i}{\sin r}$, where $i = 40^{\circ}$ and $r = 25^{\circ}$.
This gives $n = \frac{\sin 40^{\circ}}{\sin 25^{\circ}} \approx \frac{0.6428}{0.4226} \approx 1.52$.
The refractive index is also defined by the ratio of speeds: $n = \frac{v_{\text{vacuum}}}{v_{\text{liquid}}}$.
Rearranging for the speed in liquid: $v_{\text{liquid}} = \frac{v_{\text{vacuum}}}{n} = \frac{3.0 \times 10^{8}}{1.52}$.
The resulting speed is approximately $1.97 \times 10^{8}$ m/s, which rounds to $2.0 \times 10^{8}$ m/s.
Thus, option B is the correct choice based on these physical principles.
▶️ Answer/Explanation
Detailed solution:
Total internal reflection (TIR) occurs only when light travels from an optically denser medium to a less dense medium.
For a glass–air boundary, the refractive index of glass $n_{g}$ is greater than that of air $n_{a}$, meaning light travels slower in glass.
The fundamental condition for TIR is that the speed of light in the first medium must be less than in the second ($v_{glass} < v_{air}$).
Options A and B are incorrect because TIR requires the angle of incidence $i$ to be strictly greater than the critical angle $c$.
Option C is incorrect because the relationship is inverse, defined by the equation $n = \frac{1}{\sin c}$.
Therefore, statement D is the only correct prerequisite for the phenomenon to be possible.
▶️ Answer/Explanation
Detailed solution:
The refractive index $n$ is defined as the ratio of the speed of light in air (or vacuum), $v_{air}$, to the speed of light in the material, $v_{mat}$, expressed as $n = \frac{v_{air}}{v_{mat}}$.
The problem states that the speed in the material is $50\%$ of the speed in air, so $v_{mat} = 0.5 \times v_{air}$.
Substituting this into the formula gives $n = \frac{v_{air}}{0.5 \times v_{air}}$.
The velocity terms cancel out, leaving $n = \frac{1}{0.5}$, which calculates to $2.0$.
Refractive index is a dimensionless ratio, so it has no units, making option B the correct choice.