Explanation

(a) (i) The angle of incidence in the optically denser medium for which the angle of refraction in the less dense medium is 90\(^o\)

(ii) Conditions necessary for total internal reflection to occur:
- Light rays must travel from a dense medium to a less dense medium.

- Angle of incidence in the dense medium must be greater than the critical angle.

iii) Practical applications of total internal reflection

- Prism periscopes.

- Prism Binoculars.

- Fibre optics

- Fish eye view.

- Transmission of radio signals

(b) Effects of refraction

- straight objects placed in liquid appear bent (on the interface or boundary)

- mirages.

- dispersion of white light/formation of rainbow.

- apparent displacement of objects placed in liquids/apparent shadows of pools base.

(c)(i) Definition of progressive waves: A disturbance which travels through a medium that enables energy to be transferred from its source to another (without the particles of the medium transferred). OR Transfer of energy and momentum from the source of disturbances. 

(ii) (\(\alpha\)) calculation of frequency of wave

y = 0.5 sin (1000) \(\pi\) t - 100 \(\pi \frac{x}{17}\)

= a sin (2\(\pi ft - 2 \pi \frac{x}{\gamma}\))

= 2\(\pi f = 1000 \pi\)

f = 500Hz

(\(\beta\)) calculation of wavelength of wave

\(\frac{2\pi}{\lambda} = \frac{100\pi}{17}\)

\(\lambda\) = \(\frac{2 \times 17}{100}\)

= 0.34m

(\(\gamma\) calculation of speed of wave)

v = f\(\lambda\)

= 500 x 0.34

170ms\(^{-1}\)

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