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.

Electromagnetic wave emmission at Dobies

I took the picture in the depths of winter. I've been teaching about black-body emission this year. This is another good example. I say that the heater gives off infra-red. If you are close by you can really feel it. However, infra-red is not visible but the heater is clearly giving off a lot of red. This shows that electromagnetic waves are given off over a range of wavelengths. It is merely that the peak for intensity is in the invisible range. Just imagine how bright that would look to our eyes.

Bridge over the Atlantic

This bridge is from the mainland over to Seil Island just south of Oban on the west coast of Scotland. Yes, that is the sea underneath the bridge. The island is that close to the land. And if you head west from the island next stop is America so technically the sea is actually the Atlantic Ocean. So this is known as the Bridge Over The Atlantic.

Now imagine the car PARKED on top of the bridge. The upward reaction force R would equal the weight mg. When you are driving the car at a steady speed over the bridge, it will be constantly changing direction due to the curvature. It will be accelerating because acceleration is rate of change of the velocity vector. Vector includes direction change. Such an acceleration requires a centripetal resultant force. The resultant is directed downwards towards the centre of curvature so resultant force = mg - R. The faster you go, the bigger the centripetal resultant needs to be. mg can't change so the only way to get (mg-R) bigger is by R getting smaller. In the extreme case, R = 0 which means no normal contact force on the ground. You have taken off!

Ben Nevis Caldera again

 I've posted about the Ben Nevis Caldera before but this sign outside the Ben Nevis Inn gives the best explanation I've seen. Granite is formed when magma solidifies underground over up to a million years. This gives the crystals time to grow. What seems to have happened here is that granite was forming in the underground magma chamber when the top of the volcano cone collapsed in. I've seen a caldera on Tenerife. It was huge and spectacular. Trying to imagine it in this ice ravaged landscape is difficult.

Wormholes in the Solway

We walked out on the mud at Bowness-on-Solway. There were a lot of wormholes. Einstein's vision of the Universe as a curved multi-dimensional surface of space-time leads to places where the surface curves back under itself. Then it is possible for "tunnels" to be opened up between the two different sections of space-time. These "tunnels" are called wormholes. If you were able to pop through a wormhole you'd immediately appear in another place at another time, I think. That's certainly the science fiction reading of it, but I was interested to see on the Wikipedia page https://en.wikipedia.org/wiki/Wormhole that wormholes arose as solutions to the Einstein field equations. Sounds like it is back to Roger Penrose's Road to Reality book to get myself a bit closer to those equations!

Poppies at Carlisle Castle

The installation of ceramic poppies that made such an impression 4 years ago at the Tower of London has been brought to Carlisle Castle this month. It is free to visit and is proving very popular. It is very thought-provoking. I was wondering about the way that the artist has modeled the curve from the top of the keep. From the outside I thought that it looked like a parabola. Careful measurement of the photograph shows that it goes out as far as it goes down so it is probably a section of a circle.

Pressure transducer and river levels in Carlisle

We found this by the river in Denton Holme. The pressure at the bottom of the river is measured using a pressure transducer. I looked up how one of these works https://www.omega.co.uk/prodinfo/pressure-transducers.html Strain gauges are essentially wires that get stretched, making the wire longer and thinner. Since resistance = resistivity x length/cross-sectional area, the resistance changes as the shape changes. A Wheatstone Bridge is an array of 3 known resistors along with an unknown from the strain gauge, from which the unknown resistance can be calculated. Pressure varies with depth. Pressure = depth x density x g. So if the resistance of the strain gauge is calibrated for different pressures, the depth of the water can be known from the resistance.

Sea level changes at Munlochy Bay

These graphics from Munlochy Bay on the Black Isle illustrate the sea level changes in Scotland that brought about the raised beaches on Islay.

Raised beach at Kintra on Islay

I found a lovely example of a raised beach at Oban recently and reminded of these that I found on Islay last year. The idea is that the weight of the ice over the land mass during the Ice Age pushed the continental crust down. When the ice melted, it has been rebounding ever since. I have read about the ice being high enough in places so that only the peaks of the mountains can peak out. That would suggest say a 1000m deep layer of ice. Ice has a density of 917 kg per cubic metre. That would mean a pressure of 917,000 Pascals underneath. That's almost 10 times atmospheric pressure. What bothers me is that there was time for the waves to cut a flat beach platform but that has been preserved instead of there being a gradual slope as the land moves up a few cm each year.

Bond energies at Inveraray

Looking at the supermarket trolley stack at Inveraray, it finally occurred to me that this is a good analogy for calculating bond energies in Chemistry. I teach that energy is needed to break bonds and that energy is given off when bonds are remade. So I put in money to break the chain and get a trolley but I get money back when I remake the bond between the trolleys. The view was better round the corner though...