Optics: Index Refraction: Eyeglasses

Eyeglasses are an example of the usefulness of refractive index that most people are familiar with. Although contact lenses are slowly making glasses less public and more the thing that gets you safely from the bathroom to the bed at night, everyone knows someone who wears glasses.

If it weren't for the index of refraction of materials being different, we couldn't make eyeglasses. This is because the difference in the index of refraction leads to a bending of light at the interface between materials, known as refraction. How much the light bends depends on the ratio of the two mismatched indices, and is encapsulated in a fundamental law of optics called Snell's Law*.

This is useful because it allows us to make converging and diverging lenses. A converging lens is one that brings all incoming light to a tight focus; a magnifying lens is an example of a double converging lens, as any child who used one to light small fires can tell you. A diverging lens takes incoming light and spreads it out, rather than bringing to to a focus. This makes them useful for correcting short sightedness.

Optics: Refractive Index, Part 1

The refractive index of materials is one of the most obviously useful optical phenomena I can think of. We've been taking advantage of it for thousands of years, because that's how long we've used lens of some sort. The refractive index is why we have binoculars, telescopes, microscopes, eyeglasses, and why people who have really bad eye sight, like me, don't have to wear coke bottle lenses any more. Its what makes a straw in a glass of water look like its bent and that fish you are trying to catch ninja-style look elsewhere than it is. The fact that it is slightly different for different colors of light lets us use prisms to make rainbows.

High refractive index dispersive lens

So, what is this thing and how does it work?

Shower Saga, Part 1

Technically, this should be part 2 with part one here, but I didn't want to go back and change the post. 

Our ceiling is still dripping (the grout in the shower pan is acting like a giant sponge, slowly releasing its water), so our house is still full of dehumidifiers and blowers, which are starting to make it very warm, because they have been running so long. We finally got the insurance adjuster to come, and the good news is they will cover everything but the shower. I did my best to argue for it, but in the end I think it will be ok because instead of sending work crews, they send a check that covers fair market price for all the work they agree needs doing, which in this case includes the cost of professionals completely repainting my downstairs ceiling. We just finished painting it, and a relatively small section was damaged, so once the dry-wall people fix the hole, I don't think it would be too terrible to just repaint that section myself, and put the money to a new shower. 

A friend at school was able to recommend a 'good and reasonable' tile guy through a friend of his father-in-law (sometimes I love the South. Everyone has Connections). He'll come and bust out our shower base on Sunday, and when we decide what to do with the shower replacement I'm 99% sure I'll go with him. Finally things are moving towards the repaired stage of things. 

While I definitely wish that this had NOT happened right now, I am looking on the bright side, and I am learning a lot. Hopefully we can keep moving slowly but surely on this, and get it resolved quickly. 

Drip...Drip...Drip

Well, the situation has improved slightly. My house is as arid as a desert, and most of the areas that yesterday were soaking are dry.

But it's still dripping from my ceiling.

That's water, seeping through my kitchen ceiling right next to/above my fridge and stove. The shower pan is still leaking water, probably because they filled it with grout in some 80s bright idea, and then stuck little tiles on it. Grout is not water proof. It acts like a sponge. And it is now, having filled to the point it cracked and over-flowed, releasing it's water in a slow, torturous drip downstairs and a slow seeping upstairs.

The blowers and dehumidifiers are still in place to hold the seepage at bay and keep the water damage as contained as possible. The constant noise is getting on my nerves.

The only way to stop this is to remove the shower pan, which requires destroying at least the shower floor, which we can't do until the insurance adjustor comes.

Which means at least another day, and more like two, with all the noise and the dripping and not knowing when I'll be getting my kitchen back. Between all the sheetrock dust blowing around and the water dripping right where I make food I'm not comfortable cooking, so its take out for us.

I am trying to stay positive and calm. Hey, great excuse to install recessed lighting and replace the out-of-date shower! Calm and happy people are more likely to get what they want out of customer service rep types (at least in my experience). But being stuck waiting for all the parts to come together so we can get moving on repairing things is getting on my nerves.

Luckily, Penny is always there to make me and Dear husband smile. For example, reading the news of a morning on my notebook.

Because the cute dog should take up more digital and mental space than a drippy ceiling. 

My kitchen is missing its ceiling...

because the master bathroom's shower was poorly designed and now that it is 25 years old developed very small cracks in the grout which let water build up in the pan until it over-flowed and flooded my upstairs carpet and then my kitchen ceiling all in 48 horrible hours. 

It all started Saturday night as I was going to bed, and the carpet under a runner in the hall outside our bedroom door felt...squishy. Underneath, it was soaking wet. It was too late to call a plumber/the home warranty company, so I called as soon as I could Sunday morning. At this point there was just water in the upstair's carpet. I felt the kitchen ceiling--no signs of wetness/softness. Plumber diagnosed a problem with the shower basin, said we needed a restoration company/contractor,  not a plumber. So I called the insurance company, filed a claim, got the ball rolling to have an adjustor come out and assess the damage so a restoration company could take care of the (then seemingly minimal) damage.

All the water, as of Sunday night. 

 I left Monday morning, and everything seemed hunky-dory. The upstair's subflooring looked like it was drying, we weren't using the guilty shower, everything should be fine.

I came home to this

Approximately 3 ft in diameter, and has a tail that runs to the wall.

 and about two gallons of water on my floor, and a sodden kitchen island. I quickly mopped up the floor, got a bowl under the dripp, called the insurance company to tell them of the new development, the warranty company to send a new plumber, and after getting some help from a neighbor shut off the water supply to the house (it's out by the street. Never would have occurred to me to look there) tried to assess the damage. Ceiling squishy and wet. Upstairs no wetter.

Plumber came out, confirmed the first one's opinion, but with more detail. There are tiny, tiny cracks in the grout (which is not waterproof, I learned) which were letting water pool in the pan beneath, which had finally hit capacity and started to overflow. No way for us to know until it ran over.

Insurance company sent out water damage control people that evening to clean up and try to dry everything out. They started out trying to conserve as much as they could

 
 Ended up having to revise that plan when the dry wall just kept bending and collapsing.

That's a good 25-30% of my kitchen ceiling gone, and its still dripping/dusty.

Then they  set up a squadron of industrial blowers and dehumidifiers upstairs and down. 

There's another 2 that you can't see here.

 They are really loud, and they need to be going 24/7 until everything dries out. It sounds like a wind tunnel. Its pretty constant, which lets us sleep, but it is wearing, and Penny is terrified of them.

Dear Universe, when I said I wanted to redo the kitchen and the shower, I didn't mean right now.

 

Setting the Table

I've been putting off posting this for a while. I've been putting off even writing it, because I feel unqualified to offer an opinion. A small side effect of grad school I suppose.

But I feel compelled to write this. God has put this on my heart and I can't shake it.

When did the church forget our calling? When did we decide it was ok to become dictators to/slaves of social norms? When did we stop being a church of outcasts and forgiven sinners, and become the church of the middle class and 'good' people? When did we decide that we were going to ignore our call to 'the least of these', the tax collectors, the prostitutes, the criminals and the untouchables? When did we decide that we were better than everyone else and could act so high and mighty?

I know there are lots of churches who run soup kitchens, homeless shelters, prison ministries. And these are good ministries which deserve to be applauded. They are doing good work.

But if a pregnant teenager walked into your church, would she be greeted the same way you would greet a family of 4? Would the homeless man in the dirty coat be offered a cup of coffee just like the guy in the $1000 suit? Do you tell your child to stand by the gay child at school, or do you tell him to stay away?

When did we forget that we are the same as them, except that we know we have been forgiven solely by the grace of God? Is the blood of Christ sufficient only for our lying, cheating, hating, murdering, lusting, idolatrous soul, but not theirs?

If you are yelling at anyone but other believers who have defiled the church, you are not demonstrating Christ's love to the world. Who does Jesus get angry at? The Jews who turned the temple into a market. Who does Jesus show compassion to? All the sinners the 'good' people hated. He protects an adulterous woman from being stoned. Just talks to the woman living with a man who is not her husband, and offers eternal life. Eats with the tax collectors and prostitutes.

If you say that you would never do something so horrible as that, whatever sin you find particularly abhorrent, remember that in the eyes of God, a sin is a sin. Full stop. No nice gradation. Hating someone is the same magnitude as killing them. Looking at someone with lust is the same as fornication. Every day, in word, thought and deed, we sin and fall short of the glory of God. Why should I be acceptable for only lusting, and the pregnant teenager be reviled for actually fornicating? Only because we can see her sin. Secret sins are ok, so long as we keep them secret. But that is an entirely human perspective, not one of God. God sees everything, and my sin is just as deadly as her's. But Christ's blood is sufficient for me, and it is sufficient for anyone else. The quality of mercy is not strained.

The church needs to stop yelling, and start setting the table. The first literally, the latter both literally and figuratively. We need to stop turning our backs on the people who have the most claim on us, for Christ's sake. We need to offer comfort, protection and love. Not hatred and signs and things to throw. What if instead of screaming at women going to abortion clinics, we offered a coffee, a listening ear, a different path?  Defended the teenager being bullied, for whatever reason? Stopped the drunks behind the bar from beating up a guy who looks different? Gave as much to Salvation Army to help save people and get them back on their feet as we did Starbucks for a cup of over roasted coffee with over priced milk and sugar?

What if we learned to eat with the tax collectors and prostitutes?

I think it would look a lot more the like the wedding feast of the Lamb than we like to admit.

Why the Sky is Blue

So today I finally return to the world of physics and optics posts with a classic question that gets asked by children to their parents and qualifying exam committees to their examinees alike*. Why is the sky blue?

The first part of the answer is fairly easy to find with a judicious Google search: Rayleigh scattering!

In optics, several types of scattering, classified by the size of the particle doing the scattering, whether the collision is elastic (the incoming photon leaves with the same energy it started with) or inelastic (it loses energy in the collision to the thing its colliding with). Rayleigh scattering, named after Lord Rayleigh who did a lot of work in optics near the end of the 19th century, is scattering that is elastic, and the scattering object is smaller than the wavelength of the incoming photons**. The degree to which the incoming light is scattered is inversely proportional to the fourth power of the wavelength. So a longer wavelength photon will be less scattered than a shorter wavelength photon.

Sunlight is broad spectrum thermal light. For this discussion, we only care about the visible portion of the spectrum, which is roughly evenly distributed in incoming intensity. Once the sun's light hits the earth's atmosphere, it will encounter diffuse gas in the upper layers. The wavelength of the light is on the order of 10^-7  m, while the atoms it encounters have nuclei on the order of 10 ^-14 m, 10 million times smaller.

Not to scale

When the light strikes a nucleus, its component wavelengths get scattered according to the rules of Rayleigh scattering.

The red end of the light spectrum gets scattered in a roughly forward direction, while the blue/purple end of the spectrum gets scattered off to the side.  Most explanations end here, but that leaves most people wondering why the sky isn't purple.

The answer to that part of the question has nothing to do with Rayleigh scattering and everything to do with the human eye. As you can see in this link, the peak color sensitivity of the human eye is in the green (550 nm is green, 700 nm is red, 475 is blue). This is one reason why you don't see blue and purple laser pointers--our eyes don't pick them  up all that well. (Red laser pointers are the most popular because they are dirt cheap after cd players became consumer items, and because a poorly made green laser pointer emits UV laser light.) So when our eyes are presented with a little green, and a lot of blue and purple light, what we see is  blue tinged with green. If you don't believe there is green in it, go ask a painter to paint the sky for you and see if they don't include a dash of green. .

And that, my online friends, is why the sky is blue.

~PhysicsGal


*Yes, this was one of the questions in the oral portion of my qualifying exam.

**I will mention this very briefly for purposes of this post, and discuss it in greater length in a later post: light exhibits both particle-like and wave-like properties.  We can speak of photons (particle-like) being scattered elastically, but also of photons having a wavelength and frequency (wave-like).