(a) (i) Define Optical angle. (ii) Explain two conditions necessary for total internal reflection to occur. (iii) List three practical applications of total...

(a)(i) The (critical) optical angle is the angle of incidence in the denser medium for which the angle of refraction in the less dense medium is exactly 90 degrees; at this angle the refracted ray grazes the surface, and beyond it total internal reflection occurs.

(a)(ii) Conditions for total internal reflection:

• Light must travel from an optically denser medium to an optically less dense medium (from high to low refractive index).
• The angle of incidence in the denser medium must be greater than the critical angle for the two media.

(a)(iii) Applications: optical fibres (communication/endoscopes); totally reflecting prisms in periscopes and binoculars; the shining/sparkle of diamonds; the formation of mirages.

(b) Effects of refraction: a stick partly immersed in water appears bent; a pool of water or swimming pool appears shallower than it really is (real depth greater than apparent depth). (Also the twinkling of stars and apparent raising of the sun at sunset.)

(c)(i) A progressive (travelling) wave is one that moves outward from a source, transferring energy from one point to another through a medium, with the disturbance advancing continuously.

(c)(ii) Comparing with \(y=A\sin(\omega t-kx)\), the angular frequency is \(\omega=1000\pi\,\text{rad s}^{-1}\) and the wave number is \(k=\dfrac{100\pi}{17}\,\text{m}^{-1}\) (from the given equation).

(\(\alpha\)) Frequency: \(f=\dfrac{\omega}{2\pi}=\dfrac{1000\pi}{2\pi}=500\,\text{Hz}\).

(\(\beta\)) Wavelength: \(\lambda=\dfrac{2\pi}{k}=\dfrac{2\pi\times17}{100\pi}=0.34\,\text{m}\).

(\(\gamma\)) Speed: \(v=f\lambda=500\times0.34=170\,\text{m s}^{-1}\).