Read the following passage and answer the accompanying questions - Leaving Cert Physics - Question 11 - 2018

The diagram should show the Earth as a sphere with magnetic field lines:

• The field lines should emanate from the magnetic North Pole and enter the magnetic South Pole.
• The lines should be drawn as arrows pointing away from the poles, curving around the Earth, indicating the influence of the magnetic field.

Ensure that the lines are drawn with arrows indicating the correct direction of the field lines.

Information is transmitted through optical fibres via the process of total internal reflection. When light travels through the optical fibre, it hits the boundary at an angle greater than the critical angle. This results in:

• Total internal reflection, keeping the light within the core of the fibre.
• The signals can reflect multiple times within the fibre, allowing for long-distance transmission without significant loss of intensity.
• Data is encoded in light signals (pulses) that are transmitted at high speed, enabling effective communication.

Using the mirror formula:

$\frac{1}{f} = \frac{1}{u} + \frac{1}{v}$

where:

• $f = 16 \text{ m} = 1600 \text{ cm}$
• $u = -75 \text{ cm}$ (object distance, negative as per convention)

Substituting the values:

$\frac{1}{1600} = \frac{1}{-75} + \frac{1}{v}$

Solving for $v$: $\frac{1}{v} = \frac{1}{1600} + \frac{1}{75}$

Calculating this will provide the image distance $v$ (in cm).

The image of the moon will be formed at the focal point of the concave mirror if the moon is at a distance significantly greater than the focal length.

• Justification: Since the moon is far away compared to the focal length of the mirror, rays of light from the moon will approach the mirror parallel to its axis. Therefore, these rays will converge at the focal point after reflection.

The ray diagram should illustrate:

• An object placed between the focal point and the mirror.
• At least two rays from the object:
  1. An incoming ray parallel to the principal axis reflecting through the focal point.
  2. A ray through the focal point reflecting parallel to the principal axis.
• The intersection of these reflected rays indicates the formation of an upright, magnified image on the same side as the object.

The formula for calculating the velocity ( $v$) of the Hubble telescope is:

$v = \frac{2 \pi R}{T}$

where:

• $R = 6400 + 570 \text{ km}$ (radius of Earth plus altitude of Hubble)
• $T = 24 \text{ hours in seconds}$

Substituting these values will give the orbital velocity:

For $T = 24 \text{ hours} = 86400 \text{ seconds}$,

Calculate: $v = \frac{2 \pi (6400 + 0.57 \times 10^3) \times 1000}{86400} \approx 7650 \text{ m/s}$

The optical phenomenon that reduced the effectiveness of the Leviathan is refraction. Refraction affects how light travels through the Earth’s atmosphere, causing distortions.

By placing the Hubble telescope in space, above the atmosphere, these atmospheric effects are eliminated. This results in clearer images and enhances the telescope's ability to observe celestial objects without the interference of atmospheric distortions.