Read the following passage and answer the accompanying questions - Leaving Cert Physics - Question 13 - 2022

An appropriate diagram would depict a coherent light source (like a laser) aimed at a double slit, resulting in a series of light and dark bands on a screen due to interference. Each slit should be labelled, as well as the light source and the resulting pattern.

The observations show interference patterns that are characteristic of waves. When light passes through the slits, it produces alternating bright and dark fringes on the screen, which can only be explained by the wave property of light interacting with itself.

The ray diagram should illustrate a converging lens with rays coming from an object that is placed within the focal length of the lens, showing the rays diverging after passing through the lens and appearing to originate from a point behind the lens, thus forming a virtual image.

Using the formula for the period of a pendulum, $T = 2\\pi \\sqrt{\frac{L}{g}}$, we can rearrange to find $L$. With $T = 2$ s and $g = 9.81 \, m/s^2$:

$L = \frac{gT^2}{4\pi^2} = \frac{9.81 \, m/s^2 \times (2 \, s)^2}{4\pi^2} \approx 0.993 \, m.$

Using the formula for gravitational force, $F = \frac{GM}{R^2}$, we find:

1. Mass of Saturn:

   $M = \frac{gR^2}{G}$

   Substituting values:

   $R = 1.16 \times 10^6 \, m + 5820 \times 10^3 \, m = 1.22 \times 10^7 \, m$

   $M = \frac{9.81 \, m/s^2 \times (1.22 \times 10^7)^2}{6.6742 \times 10^{-11} } \approx 5.7 \times 10^{26} \, kg.$

2. Acceleration due to gravity on the surface of Saturn:

   $g = \frac{GM}{R^2}$

   $g = \frac{6.6742 \times 10^{-11} \times 5.7 \times 10^{26}}{(5820000)^2} \approx 11.2 \, m/s^2.$

3. Period of Huygens' clock on Saturn:
   Using the previously calculated length of the pendulum:

   $T = 2\pi \sqrt{\frac{L}{g}}\approx 2\pi \sqrt{\frac{0.993}{11.2}} \approx 1.87 \, s.$