CIE iGCSE Co-Ordinated Science P3.2.3 Thin converging lens Exam Style Questions Paper 3

(a)(i) Planet X is Jupiter.
From Table 10.1, planet X has a mass of \(2 \times 10^{27}\,\text{kg}\), which closely matches Jupiter’s known mass of approximately \(1.9 \times 10^{27}\,\text{kg}\). Jupiter is the most massive planet in the Solar System, making it the only candidate consistent with the table data.

(a)(ii) The Sun is 1000 times the mass of planet X — the student is incorrect.
\(\dfrac{2 \times 10^{30}}{2 \times 10^{27}} = 10^3 = 1000\). Since the ratio is 1000 and not 100, the student has made an error, likely a mistake with powers of 10. The Sun is therefore ten times more massive relative to planet X than the student claimed.

(b)(i) The two materials are gas and dust.
Protostars form when vast interstellar clouds of gas (mainly hydrogen and helium) and dust are drawn together by gravity. As the cloud collapses, temperature and pressure at the centre rise steadily until nuclear fusion ignites, marking the birth of a stable star.

(b)(ii) Stable star → red giant → planetary nebula + white dwarf.
When the hydrogen fuel in the Sun’s core is exhausted, it will expand and cool into a red giant. The outer layers will then be expelled as a planetary nebula, leaving behind the hot, dense core as a white dwarf that gradually cools over billions of years.

(c) Calculation:
\(\text{time} = \dfrac{\text{distance}}{\text{speed}} = \dfrac{1.5 \times 10^{11}}{3.0 \times 10^{8}} = 500\,\text{s}\)
\(500\,\text{s} \div 60 = 8.3\,\text{minutes} \approx 8\,\text{minutes}\) 
Therefore, the time is approximately 8 minutes.

(d) Parallel rays from the Sun enter the converging lens and refract to meet at the principal focus on the dry grass.
Since the Sun is effectively at infinity, light rays arriving at the lens are parallel to the principal axis. The converging lens bends these rays inward so they all meet at a single focal point, concentrating light energy enough to raise the temperature of the grass and ignite it.