(a)(i) What is an eclipse? (ii) List the three types of eclipse. (b) A student in a lecture theatre can read from the board clearly but requires a pair of s...

(a)(i) Eclipse: An eclipse is the total or partial disappearance of a heavenly body (the sun or the moon) from view, caused when the shadow of one body falls on another as the sun, earth and moon come to lie nearly in a straight line.

(a)(ii) Three types of eclipse:

• Eclipse of the sun (solar eclipse)
• Eclipse of the moon (lunar eclipse)
• Annular eclipse

(b)(i) Eye defect: The student sees distant objects (the board) clearly but cannot focus on near objects (the book), so the defect is long sight (hypermetropia).

(b)(ii) Correcting lens: A convex (converging) lens.

(b)(iii) Power of the lens: \(f = 10\,\text{cm} = 0.10\,\text{m}\).

\[ P = \frac{1}{f} = \frac{1}{0.10} = +10\,\text{D (dioptres)}. \]

(c) Distance between the cars: The ultrasonic beep travels from B to A and is reflected back to B, so it covers a total path of \(2d\) in \(t = 5.6\times10^{-3}\,\text{s}\).

\[ 2d = vt = 340\times5.6\times10^{-3} = 1.904\,\text{m}, \]

\[ d = \frac{1.904}{2} = 0.952\,\text{m}. \]

The two cars are 0.952 m apart at that instant.

(d) Focal length of the convex mirror: The image is virtual, formed \(9\,\text{cm}\) behind the mirror, so \(v = -9\,\text{cm}\). The magnification \(m = \dfrac{-v}{u} = 0.6\) gives \(u = \dfrac{9}{0.6} = 15\,\text{cm}\).

\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} = \frac{1}{-9} + \frac{1}{15} = -0.1111 + 0.0667 = -0.0444, \]

\[ f = -22.5\,\text{cm}. \]

The focal length of the convex mirror is 22.5 cm, the negative sign confirming that it is a diverging (convex) mirror.