(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 spectacles to read from a book.
(iii) The focal length of the lens used to correct this defect is 10cm. Calculate the power of the lens.
(c) A car B moves towards a stationary car A. If B produces an ultrasonic sound at a point and it takes 5.6 x 10\(^{-3}\)s for a beep to be heard in B, calculate the distance between the two cars at that instant. (Speed. sound in air = 340 ms\(^-\))
(d) The image of an object is located 9 cm behind a convex mirror. If magnification produced is 0.6, calculate the focal length of the mirror.
(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.
