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Table of values i^\circ \(\theta\) Cos\(\theta\) Sin i 5^\circ 81^\circ 0.156 0.087 10^\circ 74^\circ 0.276 0.174 15^\circ 69^\circ 0.358 0.259 20^\circ 61^\circ 0.484 0.342 25^\circ 51^\circ 0.629 0.423 Slope = \(\frac{x_{2}-x_{1}}{y_{2}-y_{1}}\) = \(\frac{0.6-0.1}{0.4-0.05} = \frac{0.5}{0.35}\) = 1.43 Precautions: Avoid error due to parallax The direction of the light rays must not be blocked when fixing the search pin or viewing through the glass prism The optical pins must be straight and not bend. (b)i. The first law of refraction of light states that the incident ray, the reflected ray, and the normal ray at the point of incidence all lie in the same plane. The second law of refraction of light states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for the media concerned. i.e, \(\frac{\text {Sin i}}{\text {Sin r}}\) = a constant (i1) The statement, "the refractive index of a material is 1.65" means that the ratio of the speed of light in a vacuum to the speed of light in the medium is numerically equal to 1.65. i.e; Refractive index (n) = \(\frac{\text {speed of light in vacuum}}{\text {speed of light in the medium}}\) = 1.65 The refractive index of any medium depends on the wavelength of the incident light.

When ever a ray of light is incident on a plane mirror at an angle of incidence l, if the mirror is then rotated through an angle θ, then the reflected ray is rotated through an angle twice θ So if θ = 35°, then the reflected ray is rotated through 2 x 10o = 20°

The extra lens in the terrestrial telescope mounted at the middle between the objective lens and the eye piece is to re-invert the image so that it is upright.

Thus if r = 1m f = 1/2 = 0.5m ∴ if U = - 4m (object behind mirror) f = 0.5m \(\frac{1}{u}\) + \(\frac{1}{v}\) = \(\frac{1}{f}\) -\(\frac{1}{4}\) + \(\frac{1}{v}\) = \(\frac{1}{0.5}\) \(\frac{1}{v}\) = 2 + \(\frac{1}{4}\) \(\frac{1}{v}\) = \(\frac{1+ 8}{4}\) \(\frac{1}{v}\) = \(\frac{9}{4}\) v = \(\frac{4}{9}\)

At resonance in an a.c. circuit, during which the capacitive reactance X\(_c\) is equal to the inductive reactance X\(_l\), the phase angle Ø = 0^\circ

Resonance frequency in an a.c. circuit is given by F = \(\frac{1}{2\pi \sqrt{LC}}\) therefore, \(200\times 10^3\) = \(\frac{1}{2\pi \sqrt{L\times 20 \times 10^{-12}}}\) therefore (\(200\times 10^3)^2\) =\(\frac{1}{4 \times \pi^2 \times L \times 20 \times 10^{-12}}\) THEREFORE, L = \(\frac{1}{4\times10\times (200\times 10^3)^2 \times 20\times 10^{-12}}\), (\pi\(^2\) ≈10) Therefore L =\(\frac{1}{32}\)H

The pendulum that will resonate with P is T. being of the same length and therefore of the same frequency.

n = \(\frac{\sin 45}{\sin 30} = 1.4142\) n = \(\frac{15m/s}{x}\) x = \(\frac{15}{1.4142}\) = 10.6m/s

From the diagram above, Tan\(\theta\) = \(\frac{\text{d}}{100}\) Tan10º = \(\frac{\text{d}}{100}\) d = 100 x Tan 10º = 100 x 0.1763 ≈ 17.6cm.

Convex spherical mirrors are preferred as driving mirrors mainly because they provide a wider field of view.

M = \(\frac{v}{u} = \frac{260}{20} = 13\)