(Optics) Why is lecturer in risk of getting speeding ticket?

[Mixer]

Homework Statement

An optics lecturer bought his first multifocal eye glasses a while ago. The correction for looking far away was –2.25 diopters. Compared to this, the reading part had an additional correction of +1.75 diopters to achieve the convenient reading distance of 40 cm. He also bought for driving additional glasses with the same -2.25 diopter correction. Why did the lecturer end up in a great risk of getting a speeding ticket when using the driving glasses? In the car, the distance from the driver’s face to the dashboard is 60 cm?

Homework Equations

D = 1/f , and (1/s_o)+(1/s_i) = 1/f

The Attempt at a Solution

Ok, so the lecturer is using glasses with -2.25 diopters with addiotional correction of +1.75 diopters compared to -2.25 diopters. So correction for reading is -0.5 diopters. Using lens formula I can calculate the position of formed image: s_i = (-0.5 - 1/40cm)^-1 = 1.9047 cm. So the retina is 1.9047 cm behind eyeglasses. Lecturer uses -2.25 diopter correction while driving. If the dashboard is 60 cm from the lecturer's face the location of image of that dashboard is by using lens formula: s_i = (-2.25 - 1/60 cm)^-1 = 0.44 cm. So the image of that dasboard is formed in front of retina which causes myopia. That is why the lecturer can't see the dashboard correctly thus making it difficult to see the actual speed. Is my reasoning correct here?

 

[Simon Bridge]

The real question is: how can you check that your reasoning is correct?
After all, you are training for situations where problems will potentially have unique answers or maybe no answers known (if you are ambitious). So you need some way to tell when you are spouting rubbish right?

Is there another way of reasoning?
Would the glasses affect his depth perception so that he would misjudge speeds to be a bit slower than they were (who drives to the speedo anyway right?)

Any others?

 

[Mixer]

Thank you for your reply! However my cource material won't offer me clues on how to solve this problem.. One solution could be as you mentioned that driver would see the speed to be slower than it is. But how would I show that?

 

[Simon Bridge]

Your course material should include examples of similar problems ... perhaps not posed in such a quirky way.

But what I hoped to demonstrate was the sort of thinking you need to do to reality-check your approach. In this case, unsure if the reasoning is correct, try a different reasoning.

My example was a bit toung-in-cheek ... but you'd have to consider if there is any distortion in depth measurements. Sometimes a lens may make a distant object appear farther away - if you divided the apparent distance to the object by the time to pass it you'd get a too-slow speed. If drivers cannot read the speedo (would the image really be that unclear?) then they'd have to rely on their sense of distance and time to estimate their speed. That's not too reliable anyway.

For a test or a homework problem, a good indicator is how much of the supplied information you have used ... though some people will provide too much ;)

 

[Mixer]

My cource material has no examples :(

Here is the cource material: https://moodle2.tut.fi/pluginfile.php/116692/mod_resource/content/0/Chapter5.pdf

I may be wrong, but if the objects appear farther away than they are and velocity is distance divided by time would it make velocity to seem faster? Time stays the same.

I feel so dumb :( The solution I gave is the best one I can come up. The lecturer wouldn't be able to see the speedo accurately.

 

[Simon Bridge]

That's nasty - but you are doing a course? You attend classes? Does your teacher not demonstrate with examples in class?
Moodle = online classes? (I cannot access the materials since I don't have a login.)

 

[lendav_rott]

If your lecturer is looking forward to getting an answer that is about distortion then I would immediately argue that such little distortion is no way near making a person's reading capabilities so faulty that they would misjudge the speedometer needle THAT much to get a speeding ticket. And it isn't as if they are deaf, you can hear from the sound of the engine that something is wrong - for example in the city we have max. 50 kph, that's 3rd gear for me, and I know what sound my engine does at that speed and I can tell by just looking at the tahhometer that I am speeding and just by sound if I am speeding too much.

Secondly, the police won't just ticket you for going a little over, if the limit is like 30 mph, you're fine if you do 32 or even 33, 35 is problematic but by that speed you should already feel it.

Yeah I know, I am taking into account a lot of other factors, but this assignment is just too realistic to not consider these things.
Then again, I have argued alooot of times with every single one of my lecturers.

 

[Mixer]

No, my teacher won't show any examples during lecturers and yes I do attend classes. This is not an online cource. I tried to find older versions of the lecture notes, but I failed :( But basically I know lens formula which is mentioned in first post and I know what diopter is. I also know magnification formulas.

One idea I got is that for some reason the needle of the speedometer would seem to be pointing into opposite direction than it actually is i.e if the needle is pointing to the right, the driver would see it pointing left thus making the driver think that he has a very slow speed.. I know it sounds dumb, but I'm pretty much lost with this problem :(

 

[lendav_rott]

actually that's pretty clever, if you can show that at that distance the speedometer is showing in the opposite image then you would have solved it, but the thing is, a lot of other things will appear in mirror image as well so you would be crashing long before anyone has a chance to pull you over..speaking of pulling you over, you would be turning the wrong way.

 

[Simon Bridge]

No, my teacher won't show any examples during lecturers

?? well then he must just basically read out the text. Doesn;t sound like there's much point attending.

One idea I got is that for some reason the needle of the speedometer would seem to be pointing into opposite direction than it actually is

Not bad - that would happen if the light rays through the lens swapped sides by the time they hit the eye.

Persumably you can sketch ray diagrams?

I suspect - from the extreme limited nature of the course - that the answer in post #1 is what you are expected to present. If I were you I'd also add lendav_rott's points at the end... see if you can pick up extra marks :)

 

[Mixer]

Ok, thanks I'll show the solution I got in first post next lecture. After all, that is the only reasonable solution I could come up. If it is wrong, then it is.

Thank you guys!