CIE iGCSE Co-Ordinated Science P3.1 General properties of waves Exam Style Questions Paper 4

(a)(i) Any one from:

• Satellite television transmissions.
• Mobile phones (cell phones).
• Microwave ovens.

Microwaves are a region of the electromagnetic spectrum with wavelengths ranging from about 1 mm to 1 m. They have several important applications: satellite television uses microwaves for communication as they can pass through the Earth’s atmosphere; mobile phones use microwaves for wireless communication; microwave ovens use microwaves to heat food by causing water molecules to vibrate.

(a)(ii) In a transverse wave, the vibrations / oscillations are perpendicular to the direction of propagation / direction of travel / direction of energy transfer.

Waves can be classified as transverse or longitudinal based on the direction of particle vibration relative to the direction of wave propagation. In a transverse wave, the particles of the medium vibrate at right angles (perpendicular) to the direction in which the wave travels. Examples include electromagnetic waves (including light, microwaves, X-rays), water waves, and seismic S-waves.

(b)(i) Angle of refraction = 36°.

The refractive index (\( n \)) is defined as the ratio of the sine of the angle of incidence (\( i \)) to the sine of the angle of refraction (\( r \)):

\( n = \frac{\sin i}{\sin r} \)

Given: \( n = 1.25 \), \( i = 48^\circ \)
Rearranging: \( \sin r = \frac{\sin 48^\circ}{1.25} \)
\( \sin 48^\circ \approx 0.7431 \)
\( \sin r = \frac{0.7431}{1.25} = 0.5945 \)
\( r = \sin^{-1}(0.5945) \approx 36.5^\circ \approx 36^\circ \)

(b)(ii) The ray should be drawn continuing as a straight line into the glass block in the top right region, refracted towards the normal.

When light travels from air (less dense medium) into glass (more dense medium), it slows down and bends towards the normal. The refracted ray should be drawn with a smaller angle to the normal than the incident ray (i.e., closer to the normal line), continuing in a straight line into the glass block.

(c) The ray should be drawn continuing as a straight line in the bottom right region (back into the glass), with the angle of incidence equal to the angle of reflection (total internal reflection).

When light travels from a denser medium (glass) to a less dense medium (air) at an angle of incidence greater than the critical angle, total internal reflection occurs. In total internal reflection:

• The light ray is reflected back into the glass (the denser medium).
• The angle of incidence equals the angle of reflection.
• No light is transmitted into the air.

The critical angle for the glass-air boundary can be calculated using \( \sin c = \frac{1}{n} \), where \( n \) is the refractive index of glass (approximately 1.5), giving a critical angle of about 42°. Since the incident angle in the question is greater than the critical angle, total internal reflection occurs, and the ray should be drawn reflecting back into the glass at an equal angle to the normal.