Length Definition and 1000 Threads

Homework Statement A thin film of dielectric material of refractive index 1.455 and thickness 6.50 mm is now placed over one of the slits (say the right-hand one). By how much will this change the optical path between the slit and the centre of the screen? Homework Equations Optical Path...

I believe what I am attempting to do is not possible but here goes. I want to design a fixed overall length coil which I can manually adjust the pitch on. Optimally one would be able to grab the coil and by twisting it in place would be able to change it's pitch by changing its diameter but not...

Homework Statement I need to find optical power (reciprocal focal length) of this system with thin lens Homework Equations I tried to solve this using spherical diopter equation n1/a+n2/b=(n2-n1)/R where a is object distance and b is image distance The Attempt at a Solution equation for...

Homework Statement Suppose the convex lens is placed at the 49.4 cm mark, and an image forms on the screen at the 70.5 cm mark. Find: A) The focal length of this lens: ____ cm B) the absolute value of the magnification of this lens: ________ C) the height of the image: ________cm Homework...

Homework Statement (a) Find debye frequency. (b) Find number of atoms. Homework EquationsThe Attempt at a Solution Part(a) [/B] Density of states is given by g(\omega) = \frac{3V\omega^2}{2 \pi^2 c^3} = N \left[ \frac{12 \pi \omega^2}{(2\pi)^2 n c^3} \right] = 9N \frac{\omega}{\omega_D^3}...

Homework Statement Calculate the focal length of 1D Fresnel lens, whose transmittance is given as $$T(\xi)=\frac 1 2(1+\cos(\alpha \xi ^2)).$$ Homework Equations Anything you wish The Attempt at a Solution I have no idea. I tried to use the equation for diffraction image $$u_p=C\int _0...

I was doing some calculations earlier and tried the ratio between a metal's fermi temperature ##T_F## and debye temperature ##\theta_D##: \frac{T_F}{\theta_D} = (6 \pi^2)^{\frac{1}{3}} \left( \frac{\lambda}{a} \right) where ##\lambda = \frac{\hbar}{2 m_e c}## and lattice spacing is ##a##. I...

As I am sure everyone is aware, there are still folks who don’t believe SRT and GRT. While 99.9% of them are nut-jobs, there is at least one that I respect – Tom Phipps specifically. I am not familiar with any of his writing before the advent of the GPS satellites. In any case, he now accepts...

>Two wires of the same material are both connected to a 9-V ideal battery. They have the same cross section area but wire 2 is twice longer than wire 1. Compare the following quantities by answering if the quantity for wire 1 is smaller, equal or greater than the same quantity in wire 2. > -...

Homework Statement There are three subquestions in this question, all marked bold. Let's consider a gradient index lens of thickness ##d##, whose refractive index changes with the distance from the axis with the following formula $$ n(r) = n_1 + a r^2 $$. Determine the lens's focal length...

Homework Statement Hi everybody; a teacher of mine has given me a photo of two street lampd and their shadows; he has said to me that it's height is 3 metters, and the distance between the lamps is metters, and with that information I should be able to tell the length of the shadow. The image...

MODERATOR NOTE: THERE IS NO TEMPLATE BECAUSE THIS THREAD WAS ORIGINALLY MISPLACED IN A NON-HOMEWORK FORUM Viscous liquid (ρ = 1460 kg/m3, μ = 5.2×10−1Ns/m2) is pumped through a smooth pipe with a 0.1 m diameter, at a rate of 5×10−2m3/s. Using your Fanning friction factor versus Reynolds Number...

Homework Statement If you have a ring of charge, is it valid to say lambda = Q/L, or is it lambda = dQ/dL? Homework EquationsThe Attempt at a Solution

Homework Statement A 1.0m long rod of metal has a diameter of 0.75 cm. This metal has a coefficient of linear expansion α = 4.8 × 10−5 1/K , a density of 9.7 × 103 kg/ m3 , and a heat capacity of 390 J/K . How much energy needs to be added as heat to increase the length of the rod by 7.5 × 10−3...

Homework Statement 1) The medium-power objective lens in a laboratory microscope has a focal length fobjective = 3.70mm . If this lens produces a lateral magnification of -42.5, what is its "working distance"; that is, what is the distance from the object to the objective lens? 2) What is the...

Premise 1: Line is composed of points. Premise 2: Each point is associated with specific co-ordinates (x,y). Premise 3: Lines of equal length have equal number of points. Lines of greater length have greater number of points. Premise 4: Each value of x in the function f(x) gives a single...

Premise 1: All straight lines have the value of length equal to the numerical value of the end point, provided the starting point of the line is assigned the numerical value zero. Premise 2: No point can be assigned the value y.xxxxxx... or y.abcdef...(Example: 8.9999... or 8.39465..). We...

Homework Statement A length of wire, length l, is clamped at its midpoint. It is then stretched on the right side, with the left side unchanged, to a length of l (the right side has a length l). The original Resistance of the wire was R, what is the new resistance of the wire? Homework...

I seem to be missing something fundamental about length contraction in SR. I would be grateful if someone can point out the error in the following logic. Suppose I have a method to measure lengths of objects in the following manner: I place a mirror at the right end of the object, send a light...

Homework Statement We were shown this image ^ We were later told that it is suggested that the depression (y), is directly proportional to the length of the beam cubed (L3). We were asked to give reasons why this is so. EDIT: The 1kg mass is placed at L/2 Homework Equations y is directly...

-Hello everyone. At school, I studied about convex lense and concave lense. They are very interesting, we learned about how lights would be after going through the lense. But what I want to ask is how we can calculate the distance between optical center and focal (I means focal length). Focal...

Hi all, I am reading some materials on the scattering. There is simple model to consider atom as a rigid body but with radius replaced by the so-called scattering length. I didn't learn the scattering theory systematically but my understanding on the scattering length is the minimum separation...

Homework Statement A mass of 0.36kg hangs motionless from a vertical spring whose length is 0.8m and whose unstretched length is 0.51m. Next, the mass is pulled down to where the spring has a length of 1.09m and given an initial speed upwards of...

I need to reduce the beam diameter of a laser I am using. I plan to do this by first passing the beam through a positive spherical lens with focal length f1 and then a negative spherical lens with focal length f2 and f2 < f1. By placing the lenses so that the two focal points overlap I will have...

A sad and strange image, I know, but better than none at all. What you see is a stake I'm trying to model using CAD software. With the dimension given (5 inches--in case it's not clear, the distance from the top of the equilateral triangle that encloses this shape to the midpoint of the red arc)...

Question: A copper wire and steel wire with identical diameters are placed under identical tensions. The frequency of the third resonant mode for the copper wire is found to be the same as the frequency of the fourth resonant mode for the steel wire. If the length of the copper wire is 3.44 m...

The arc length of any curve defined by ##y = f(x)## is found as follows: $$ds = \sqrt{dx^2 + dy^2}$$ $$ds = \sqrt{dx^2(1 + {\frac{dy}{dx}}^2)}$$ $$ds = \sqrt{dx^2} \sqrt{1 + [f'(x)]^2}$$ $$ds = \sqrt{1 + [f'(x)]^2} dx$$ Isn't ##\sqrt{dx^2}## equal to ##|dx|##, and not ##dx##?

Left picture: There are two moving rails that cross at center (red dot) which itself doesn't move. The rails speeds are close to c, so that they are length contracted by factor 10 (roughly 0.995c). There are markings in rails at interval 10 length units in rails rest frame, so the interval is...

$\triangle ABC$,with $\angle A=70^o,$point $O$ is the midpoint of segment $\overline{BC}=12$ circle $O$(wth center $O$ and radius $\overline{BO})$, meets with $\overline{AB},\overline{AC}$ at points $E$ and $F$ respectively please find the length of arc $EF$

Hi, I have a task and don't know the good solution. (I add the picture of my task.) I need to find the right length and deflection and to check if the results didn't exceed the allowable stress. I know the value of "q" (force). Also I could choose myself the lenght, but I need to check, if my...

Homework Statement A collimated beam from a white-light source is incident normally on a transmission grating with 500 lines per mm. The transmitted light then passes through a lens which is used to project the visible (380–780 nm) spectrum of the light source on to a strip of photographic film...

Homework Statement What is the focal length of a dewar window distorted by a pressure difference? As a result of the pressure difference, the radius of the first surface of the window is R1 = 100 meters. The window is 3 mm thick, with an index n = 4 at l = 4 um. Homework Equations I think I...

Hey guys, I'm currently working a take home problem that's a little different then what I have been practicing in my Calc. book. I thought I set it up correctly, but yet I am not getting the correct answer. Can someone show me where I am going wrong? This is what I have so far.

Homework Statement [/B] We are given a graph, with the information of the period, and the radius of the string. We amassed this data on our own. The graphing of it is quartic, but we have to make it into a linear graph?Homework Equations N/A The Attempt at a Solution [/B] First we tried to...

I'm given an irregular shaped plot with 3 sides, and have been asked to find the fourth missing side, no other detail is given. Is it possible to find the missing side? If so, then how? Here is what it looks like roughly:

Homework Statement Find the arc length of: r(t)=<e^t, e^(-t),sqrt(2)*t> from 0 to ln(2) Homework Equations L=integral from a to b of the magnitude of r'(t) The Attempt at a Solution Okay, this was an Exam question, the one exam question that I could not get on our Calc 3 exam. This breaks...

Arrange these bonds in order of increasing bond length. C-I, C-Br, C-Cl, C-F Is there a way to figure this out without drawing molecular orbital diagrams and determining the bond order?

Hey guys. Could anyone give me an what the criteria for minimum engagement length of a bolt is? The bolt I'm using is M10x1. Thanks!

Hopefully I can word this correctly. Consider viewing S11 of a short on a smith chart. It starts at the left and moves clockwise around the edge. If you then add a small length of line between the reference plane and the short, the phase angle wraps further around the outside in the clockwise...

I have one question from my mathematics for machine technology book that has me stumped as well as my Father in-law, sister in-law and my accountant friend. I wasn't sure if I was supposed to create a right triangle and use A² + B² = C² Problem 18. B...

Homework Statement A thin double convex lens of focal length f is broken down into two halves at the axis. The two haves are then combined, as shown in the figure. What will be the focal length for the arrangements...

Homework Statement The barrel of a compound microscope is 15.9 cm in length. The specimen will be mounted 1.17 cm from the objective, and the eyepiece has a 5.00 cm focal length. Determine the focal length of the objective lens.Homework Equations I am using the mirror equation. The Attempt at...

Hello guys I am working on designing somethings and I am using metal tubing. I do not know what type of metal tubing I am going to use this all depends on the math after I work my problem out. I am not sure what formulas to look up or what strength test I need to look up. For example if I have...

Lorentz believed in the ether, and developed his version of Relativity Theory based on interactions of moving charged particles (electrons, specifically) with the ether. What I don't understand is how one always gets length contraction for movement in an inertial system moving with respect to...

hello,If anyone of you help me in finding specification(diameter of nichrome wire required) for a 2 m nichrome wire to heat up to 65 degree Celsius .Voltage applied is 12 v. I want to use it by coiling it to cylindrical mica sheet to make a smaller heating product.Temperature should not exceed 65.

Homework Statement Find the arc length of r(t)= <tsin(t), tcost(t), 3t> from 0 to t to 2pi (inclusive) Homework Equations Integral from 0 to 2pi of the magnitude of r'(t) dt The Attempt at a Solution 1. Must find the derivative of the function. Using the product rule a few times, the...

I understand this that when an object is kept at focus of convex lens, then image is formed at infinity. So when we keep a convex lens above plain mirror and move object needle on the principal axis of convex lens and see a coinciding image with needle on lens and measure distance from lens then...

Hello, I am currently taking Organic Chemistry and was wondering what is the relationship between bond length, hybridization, and resonance? In other words, do some hybridization have smaller bond length? How is that affected by resonance?

Homework Statement Radio waves travel at the speed of light waves (3.00 *10^8 m/s). If your radio is tuned to a station broadcasting at 1250 kHz, what is the length of the waves arriving at the radio antenna? Homework EquationsThe Attempt at a Solution i can find the wavelength but i don't...

As we know force =mass*acceleration & force =BIL. Can we make this equation as ma=BIL?