Refraction in the fish tank

Look at how this fish tank at Maryport Aquarium appears to narrow very quickly, far more quickly than perspective would allow. I've been working on a ray diagram:

Light from each end has to bend to reach the same eye, meaning for the angles of refraction that r2>r1. This means that the ray with angle r2 is showing you a piece of the back wall that is further back than the distance between the two normal lines on the front wall. I added the dotted blue lines with the idea that the brain can't cope with light bending and makes it so that what we see is as if the light had gone straight. This accentuates the effect described above.

Sundog at sunset

Two days ago at sunset I spotted a sundog on the horizon. In the photograph above it is not the prominent bright spot in the middle of the grey cloud - that's a reflection. It's level with the Sun and one third of the way in from the right just above the hedge. There have been a lot of sundogs this year but with this one, it struck me that it seemed an awfully long way from the Sun, more so than usual. Celestial distances seem exaggerated close to the horizon. For example, the Moon seems much bigger when low over the horizon. So I measured the angle as shown below. Thumb to little finger is about 20 degrees. The sundog is always 22 degrees. Below the sundog is just past my little finger, so it's right.

Sunset on the longest day

Sunset on the solstice was almost 10pm BST and here the sun set in the north west. It's wonderful having sunlight all evening. I was reading about summer solstice in Barry Lopez's book Arctic Dreams. He points out that on the summer solstice at the exact geographic North Pole, the Sun would go round in a circle at the same height above the horizon for 24 hours. It stands to reason but is still amazing.

U-value of a thatched roof

We came across thatching in progress and were amazed at how thick it is. I'd never seen a cross-section of thatch before. U-values are used to measure the effectiveness of an insulation material. The rate of heat loss = area x u-value of insulation x temperature difference between inside and outside. Thus u-value is measured in Watts per square metre  per degree Celsius and the lower the u-value, the better the insulation because the fewer the Watts are lost. According to one website, the maximum allowed u-value is 0.15 https://www.thegreenage.co.uk/getting-to-grips-with-u-values/ I found a site with values for thatch https://www.uttlesford.gov.uk/CHttpHandler.ashx?id=2139&p=0 which gives 0.29 and 0.23 depending on the reed used. So a thatched roof on its own does not meet current regulations and would need internal insulation. But it's not far off. The trapped air between the reeds acts a good insulator.

Pressure at the fountain in Lancaster

We found this fountain in Williamson Park in Lancaster. I'm estimating that the water fountain goes up 4 metres. By using the idea that kinetic energy turns into gravitational potential energy or 1/2mv^2=mgh, you get v = sqrt(2gh). So the velocity of the water coming out of the nozzle is about 9 metres per second. Volume flow rate in cubic metres per second = cross-sectional area of hole x velocity. I'm going to estimate a cross-sectional area of 1 square centimetre or 1 x 10^-4 square metres so volume flow rate = 9 x 10^-4 cubic metres per second. Mass flow rate = density of water x volume flow rate = 0.9 kg per second since the density of water is 1000 kg per cubic metre. Newton's second law says that force = rate of change of momentum = mass flow rate x velocity = 0.9 x 9 = 8N. Pressure = force per unit area = 8/1 x 10^-4 = 80000Pa.

Pine tree cantilever oscillations

I watched the pine tree in the centre right of photo oscillating freely after being driven by the wind. I timed 6 oscillations in 27 seconds, so time period was 4.5 seconds. I looked for an equation and found one here
https://physics.stackexchange.com/questions/171198/derive-equation-for-a-cantilever-in-shm
Time period = 6.19*L^2/d x sqrt(density/Young Modulus). I looked up density of pine (510 kg per cubic metre) and Young Modulus of pine (9GPa). I d is the width of a rectangular cross-section. I used diameter instead which I estimated at 0.15m, though it is not uniform. I get a length of 21m. I think that's probably a bit big but not by much!

Distance and displacement at Burnham Overy Staithe

These Shelduck were making interesting tracks in the mud, crossing backwards and forwards over the places they had already walked. They had walked quite a long way but hadn't ended up far from where they started. Distance is a scalar quantity and is the actual length they have walked. Displacement is a vector and is just the distance measured in a straight line from the start point, with direction from the start given.