Solution:
To calculate the distance, we use the formula:
\[ \text{Distance} = \text{Speed} \times \text{Time} \]
Given:
Speed of sound = 340 m/s
Time = 3.50 s
\[ \text{Distance} = 340 \times 3.50 = 1190 \, \text{m} \]
Therefore, the distance between the student and the firework is 1190 m.

Answer:
The student can use a stopwatch to measure the time between seeing the light and hearing the sound.

Explanation:
The speed of light is extremely high (approximately \(3 \times 10^8 \, \text{m/s}\)), so the time taken for light to travel even a short distance is too small to measure accurately with a stopwatch. The time difference between seeing the light and hearing the sound is primarily due to the much slower speed of sound, not the speed of light.

Solution:
The refractive index (\(n\)) of the glass can be calculated using Snell’s Law:
\[ n = \frac{\sin i}{\sin r} \]
Where:
\(i\) = angle of incidence in air = 42°
\(r\) = angle of refraction in glass = 29°
\[ n = \frac{\sin 42°}{\sin 29°} \]
Using a calculator:
\[ \sin 42° \approx 0.6691 \]
\[ \sin 29° \approx 0.4848 \]
\[ n = \frac{0.6691}{0.4848} \approx 1.38 \]
Therefore, the refractive index of the glass is 1.4 (to two significant figures).

Explanation:
At point X, the ray of light is traveling along the normal (perpendicular) to the boundary between the two media. When light travels along the normal, it does not change direction because the angle of incidence is 0°, and thus, there is no refraction.

Answer:
The type of reflection that occurs at point Y is total internal reflection.

Answer:
One use for optical fibres is in communication, such as transmitting data over long distances in telecommunications.