Solving Problem $6$: A Step-by-Step Guide

[newsun]

Please help me with problem $6$ in here

 

[Simon Bridge]

Welcome to PF:
There are six exercizes there related to concepts about how light refracts, reflects, moves etc.
However, we cannot know how to help you if you have not attempted any of them.
Show us what you have tried.

For instance - #1 is about Snell's law

Note1: Your title really needs to be related to the problem. "Help me" is not very informative: that's what we are here for.

Note2: it is often considered poor nettiquette to post attachments in proprietary restricted formats - especially ones that are notorious vectors for viruses. Not everyone has Microsoft Word to read doc files with - so they have to use Google Docs or something. Fortunately this one would open in Libre Office. It is best practice, when you want help, to make it as easy as possible for someone to help you.

 

[Evo]

Quoting for record.

Please help me with problem $6$ in here

Nature of light
Exercise 1:

John would like to swim from A point on the bank of a river to B point on the other blank side (Fig.1). The distance from B to the blank of the river is h, and the width of the river is r.
If v1 and v2 are John swimming and running velocities, respectively. Determine the shortest time that John reach the B point if the distance from A to B along to the river blank is l.

Figure 1.
Exercise 2:
In an experiment of measuring diffraction factor of a pyramid we use a light as source and light to the edge of the pyramid. After changing the angle of the coming in light we have the going out light make a symmetric position in comparing with the pyramid.
The opening angle of the pyramid and the going out light are α and β, respectively (Fig. 2).
Determine the diffraction factor of the pyramid material.
Figure 2.
Exercise 3:
In a rain we could hear the sound of the thunder 6 seconds later than we had seen it. Calculate the distance from us to the thunder position.

Exercise 4:
In some story, they sometime saw the images of cities on the cloud when got lost on the deserts. The reason was that, the diffraction factor of the air at those desert decreases depend on the height. Consider the diffraction factor depends on the height as next function: if n0, a, b are constants.
Calculate the nearest city that would be seen and the highest point that a light reflect.
Exercise 5:


Estimate the thickness of a bubble
Exercise 6:
Newton’s Rings:
Figure 6 shows an image given by so called Newton ring experiment (upper) and schematic set up of the experiment (under). Light with wavelength λ goes through a curve surface, which has spherical r = 100 cm radius, reflects at planar surface and gives red rings shown in upper plan (Fig. 6), which have radiuses shown in next table:
No R(cm)
1 1.77
2 3.10
3 4.01
4 4.73
5 5.43
6 6.02
7 6.48
8 6.95
9 7.12
10 7.88
Calculate the wavelength with measurement error.

Figure 6

 

[newsun]

Thanks for all of replies. Now 6 problems are clear. Can you give me some hints of answers for these..

 

[Simon Bridge]

I like #5: the image shows a very clear upright image and asks to estimate the thickness.

I suppose I could help out and upload a pdf, or something, of the document but the original turned out to be clean and easily read, no nasty undocumented stuff in there, so it was no biggie. In that case it is kinda tricky to know whether to say anything... I just erred on the side of knowledge over ignorance.

 

[Simon Bridge]

OK: Hints:

1. You need to know Snell's Law and what "refractive index" means.
2. You need to know what a "diffraction factor" means for a prism.
3. You need to know the speed of light and the speed of sound.
4. Also diffraction factors: how do mirages work?
5. Is the image in the bubble the result of reflection or refraction?
6. Experimental methods - use the data to make a graph in such a way that the slope of the graph tells you want you need to know.

 

[Evo]

Newsun, you didn't fill out the template and you made no effort at solving the problem. No one is allowed to help you until you tell us what you have tried already and where you are stumped.