Physics 2012 Jamb Examination

Given: y = 15 sin 2π5 (60t - x).

comparing  y = 15 sin 2π5 (60t - x) with the equation of wave motion Asin2πλ(x - vt)

$$\dfrac{2π}{5} = \dfrac{2π}{λ}$$

Therefore, λ = 5m.

The velocity of sound in air depends mainly on the properties of the medium, such as temperature, humidity, and the motion of the air itself. Pitch and loudness are properties of the sound wave and do not influence its speed. When wind moves in the same direction as sound propagation, it effectively increases the relative speed of the sound with respect to the ground. Therefore, the motion of the medium (wind) affects the velocity of sound.

The intensity of a vibration is proportional to the square of its amplitude. A larger amplitude means the vibrating particles of the medium move farther from their equilibrium positions, thereby transferring more energy per unit area per unit time. Frequency and wavelength determine the pitch and tone, not intensity.

A concave mirror produces an enlarged and upright image when the object is placed between the pole and the principal focus. This is because the reflected rays appear to diverge from a virtual image behind the mirror. Shaving mirrors use this principle to magnify the image of the face for better visibility.

The magnification of a pinhole camera is given by the ratio of the image height to the object height, which equals the ratio of image distance to object distance:\[\dfrac{h_i}{h_o} = \dfrac{v}{u}\]Here, \(h_i = 2.5 \; \text{cm}, \; v = 5 \; \text{cm}, \; u = 300 \; \text{m} = 30000 \; \text{cm}\).\[h_o = \dfrac{h_i \times u}{v} = \dfrac{2.5 \times 30000}{5} = 15000 \; \text{cm} = 150 \; \text{m}\]The height of the building is 150 metres.

A plane mirror always forms a virtual image of the same size as the object, irrespective of the distance. Hence, the magnification, defined as the ratio of image height to object height, is always 1 for plane mirrors.

The sun is effectively at infinity, so the rays arriving at the concave mirror are parallel to its principal axis. Parallel rays incident on a concave mirror are reflected through its focal point, hence they converge at the focus.

The apparent displacement \(d\) is given by:\[d = t \left(1 - \dfrac{1}{\mu}\right)\]Assuming the refractive index of glass \(\mu = 1.5\) and \(t = 10\; \text{cm}\):\[d = 10 \left(1 - \dfrac{1}{1.5}\right) = 10(1 - 0.667) = 3.33 \; \text{cm}\]Thus, the object appears displaced upward by 3.33 cm.

For total internal reflection to occur, two conditions must be satisfied:
1. Light must travel from a denser medium to a rarer (less dense) medium.
2. The angle of incidence must be greater than the critical angle.
These correspond to statements II and III, respectively. Statement I is incorrect because total internal reflection cannot occur when light travels from a less dense to a denser medium.

A periscope typically uses plane mirrors for reflecting light to allow observation from a hidden position. Projectors, the human eye, and telescopes all use lenses for image formation. Therefore, the periscope is the only device among the options that does not use lenses.