In optics, a thin lens is a lens with a thickness (distance along the optical axis between the two surfaces of the lens) that is negligible compared to the radii of curvature of the lens surfaces. Lenses whose thickness is not negligible are sometimes called thick lenses.
The thin lens approximation ignores optical effects due to the thickness of lenses and simplifies ray tracing calculations. It is often combined with the paraxial approximation in techniques such as ray transfer matrix analysis.
My picture is here:
The diameter ##D## is also a diameter of the lens.
If there was no shade, the image of the moved source would be by using ##\frac{1}{2f}+\frac{1}{L}=\frac 1f## at a distance ##L=2f##. So by using a triangle similarity we get
##\frac{D/2}{L}=\frac{d/2}{L-l}##,
so...
From ray tracing I would say that the image is upright.
Using the equation ##\frac{1}{p}+\frac{1}{q}=\frac{1}{f}## with ##f=-\frac{R}{2}=-2## and ##M=-\frac{q}{p}=\frac{3}{4}## I get ##p=\frac{2}{3}cm\simeq 0.67 cm##.
Is this correct? Thanks
I created the following ray diagram to help me solve the problem:
Then I applied the mirror equation 3 separate times.
However, the final image distance I got is wrong. I'm wondering if I'm mistaken in taking the last object distance to be negative. However I only have one more try to get this...
Homework Statement:: Finding the distance between the back surface of the first lens and the front surface of the back lens.
Homework Equations:: 1/f = 1/s_o + 1/s_i
I have two positive thin lenses that are separated by a distance of 5 cm. The focal lengths of the lenses are F_1 = 10 cm and...
I tried -M=pq = f/(f-p) = f/f - f/p = 1-(f/p)
=> M+1= -f/p
=> -Mp-p=f
But since it’s the y intercept, p will equal zero and so the focal length will be 0?
Hello,
suppose we are given a thin lens and consider an image of some object formed by that lens. I am wondering what would happen to the image if the thin lens is flipped around (180 degrees)? Of course, if the lens is perfectly symmetric -like for a bi-konvex lens- then the picture should not...
Hello,
in geometric optics people usually say that the refraction of light beams due to a thin lens can be handled by introducing a hypothetical plane (the so called principal plane) at which all the refraction can be considered to happen. But most books only picture the situation for symmetric...
So we are studying optics in school this semster, Very interseting topic I say but I just have a couple of question I want to ask.
In concave and convex mirror, we study spherical ones where F = R/2. I was able to prove this and that it is only an approximation when ## R >> h_o ## or ## h_0##...
Homework Statement
Homework Equations
We will call ##s## the distance of the object from the first lens, ##s'## the distance of the image from the first lens and ##s''## the distance of the image from the second lens.
The Gauss's lens equation:
$$\frac{1}{s} +\frac{1}{s'}=\frac{1}{f_1}$$...
Homework Statement
Hi everybody! Being given three identical thin lenses with the same focal length, I have to determine ##a## (distance object-screen), ##d_a## (distance lens 1-lens2) and ##d_b## (distance lens 2-lens 3) so that a sharp image of the object appears on the screen regardless of...
Why isn't 1/f=1/do+1/di just the mathematical equivalent to f=do+di? Can't you raise all terms in the equation to the power of negative 1 to get the latter equation? The maths of reciprocals is confusing me lol.
Homework Statement
Consider a double slit experiment with a light source of 540nm. Slit separation is 4mm. A thin glass plate is placed in front of one of the slit,, resulting in each bright fringe moving to the location of the adjacent bright fringe. Find the minimum thickness of the glass...
I was browsing about my optics books,completing numericals and stuff
When I found a a statement called different lens formulas
It had 2 formulas
One,called the thin lens formula or rather the geometric sign convention formula was called 1/v-1/u=1/f(Symbols have their usual meanings) and another...
Homework Statement
A thin lens is placed 2m after the beam waist. The lens has f = 200mm. Find the appropriate system matrix.
This is a past exam question I want to check I got right.
Homework Equations
For some straight section [[1 , d],[0 , 1]] and for a thin lens [[1 , 0],[-1/f , 1]]...
Homework Statement
Write the Radiative Transfer Equation for an isotropic incoherent point source a distance p away from a thin lens. Assume that scattering in air can be ignored but absorption cannot be ignored.
Homework Equations
1. Radiative Transfer Equation (RTE):
\frac{dw}{dt} = \left[...
Homework Statement
i need to couple a ray (point source 15 deg) into a fiber with a small core diameter, the fiber located 8cm from the source.
the focal distance of the lens is 1.5cm
i need to choose 2 possible locations
Homework EquationsThe Attempt at a Solution
first suggestion:
i placed...
Hello,
I've come across an problem that requires the lens to be at least about 350 mm away from the object.
Object to be examined is 80 mm tall and imaging plane is either 11 mm or 25 mm tall. I've tried to calculate required focal length, but have not succeeded. Distance from lens to imaging...
Homework Statement
An object 4.29 cm high is projected onto a screen using a converging lens with a focal length of 32 cm. The image on the screen is 51.7 cm. Where are the lens and the object located relative to the screen?
ho=4.29 cm
hi=51.7 cm
ƒ=32 cm
Homework Equations
1...
Homework Statement
Now consider a diverging lens with focal length f=−15cm, producing an upright image that is 5/9 as tall as the object.
What is the object distance? You will need to use the magnification equation to find a relationship between s and s′s′. Then substitute into the thin lens...
Homework Statement
For those fortunate souls who do not need glasses, the lens of the eye adjusts its focal length in order to form a proper image on the retina. This typically means that very distant objects as well as objects as close as 25 cm can be seen clearly.
Many of us need...
Homework Statement
Hi all. This is a problem from one of the problem sheets from earlier in the term. I'm just revising for my exam tomorrow and can't solve this one. Here it is:
Consider a light source placed at a fixed distance L from a screen, such that a lens of focal length
f can be...
Homework Statement
I am given 5 distances to place the object relative to the lens. I then need to calculate each of the images distances for all 5 and record them. Once I have that done, I am to conduct a graph of 1/q vs 1/p. I then need to answer these questions:
1- Is the slope of your...
Hi
The thin lens equation we know is given by
\frac{1}{S_O} + \frac{1}{S_I} = (n-1)(\frac{1}{R_1}-\frac{1}{R_2})
assuming light is incident from air. The "usual" way to derive the thin lens formula (aka the Gaussian Lens Formula) is to say that when looking at the system when either the...
'm currently reading chapter 27 of the Feynman lectures, where he derives the thin lens equation for a single refracting surface. He arrives at the equation
h^2/2s + nh^2/s' = (n-1)h^2/2r
Where s is the object distance, s' is the image distance, n is the index of refraction of the second...
Homework Statement
A lens is a transparent refracting medium bounded by two spherical surfaces.R1 and R2 are radii of two surfaces.
Homework Equations
Will the Radii R1 and R2 will be same or different ?
The Attempt at a Solution
I hope that they are same, otherwise there won't...
Homework Statement
A light source placed in the focus of a (thin) lens with a focal length of 50mm.
A second (thin) lens (with focal length = 400mm) was placed 600mm after the focal point of the first one, an image of the light source was captured at the seonds lens focal point. How...
Homework Statement
Determine the focal length of a plano-concave lens (n=1.5) which has a radius of curvature of 10 cm. What is its power in diopters?
Homework Equations
None given.
The Attempt at a Solution
1/f=(n-1)(1/R_1-1/R_2)=(1/2)(-0.1)=-1/20.
Thus f=5 cm and P=-20 m^(-1)...
Homework Statement
Show that the minimum distance between 2 conjugate points (real object and image) for a positive thin lens is 4f.Homework Equations
\frac{1}{f}=\frac{1}{S_o}+\frac{1}{S_i}.The Attempt at a Solution
I assumed the lens to be biconvex (though I know that I can't. There are so...
Hi, in questions involving lenses, when using the "thin lens formulae"
if my di is negative doesn't that mean the image is on the other side of the lens?
in this example however it doesn't seem this holds true..
A doctor examines a patient's skin lesion with a 15 cm focal length...
Homework Statement
Under what conditions will a thin converging lens form:
a) a real image,
b) an inverted image,
and c) an image smaller than the object?
Homework Equations
none
The Attempt at a Solution
I have concluded that:
a) the object needs to be outside the focal...
Hi guys
I wonder if you can explain this to me. In http://en.wikipedia.org/wiki/Ray_transfer_matrix_analysis#Table_of_ray_transfer_matrices it says under "Thin lens" that the ray matrix is given by
\left( {\begin{array}{*{20}c}
{r_{final} } \\
{r_{final}^' } \\
\end{array}} \right) =...
Homework Statement
A small fish, four feet below the surface of Lake Lansing is viewed through a simple thin converging lens with focal length 30 feet. If the lens is 2 feet above the water surface, where is the image of the fish seen by the observer? Assume the fish lies on the optical axis...
Homework Statement
part1: In the Figure below a lens of focal length 8 cm is placed between a plane mirror and a pin hole. The other side of the pin hole is illuminated by a light source (not shown), so that the light passes through the hole and is then collected by the lens. If the pin hole...
Homework Statement
A student is working in an optics lab and has a light bulb which is 100 cm from a screen. She needs to make a real image a real image of the bulb on the screen and she has a converging lens with a focal length of +15 cm. Find two places she can put the lens and give object...
Homework Statement
Heres the problem exactly as written:
A system of lenses is composed of three lenses. Calculate the maximum magnification these three lenses will achieve if the lenses are located 35.0 cm apart. The lenses have focal lengths of 15.0, 20.0, and 25.0 cm.Homework Equations
1/p...
Three questions:
1) Anyone have a pedagogic answer to why the image formed by a thin lens is inverted (i.e. upside-down)? I realize that to get a focused image, the lens has to converge the rays one way or another, so then, eventually, the rays have to cross the optic axis, which in turn...
If you want to produce an image of a bulb that is enlarged by a factor of 2, how far from the wall should the lens be placed. Focal length is 40cm.
I know you use 1/d_o + 1/d_i =1/f and m= -d_i/d_o but how do you find d_o? -2/d_o +1/d_o =1/f ? but it comes out to 40cm and not 60cm...
kk so i found out the steps involved deriving the thin lens equation, but what i don't get is when you have 2 similar triangles say triangle abd,edf are congruent how does the 2 triangles make it so its di/f-1. so what I am basically asking is can someone thourougly explain to me what's going on...
Hi I need help on figuring where and how 1/f = 1/do + 1/di
My teacher told me it relates to the ray diagram but i have no clue where to start to find where this formula has come from. Any help would be much appreciated.
Hi, I was reading a section which explains about the
"thin lens equation for diverging lenses" and it included an example;
Formula:
1/f = 1/di + 1/do
where f is the focal distance,
di is the distance of the image from the center and,
do is the distance of the object from the center.
Example:
f...
Homework Statement
Hi, I am writing a lab report, and I have no idea how to come up with a fitting hypothesis for this lab
Purpose: To determine the relationship among the focal length, the image distance, and the object distance of a converging lens.
Homework Statement
A source S of monochromatic light and a detector D are both located in air a distance of h above a horizontal plane sheet of glass, and are separated by a horizontal distance of x. Waves reaching D directly from S interfere with waves that reflect off the glass. The...
Homework Statement
3. A converging lens has a focal length of 10 cm. A screen is placed 30 cm from an object. Where should the lens be placed, in relation to the object, to produce a focused image?Homework Equations
1/do + 1/di = 1fThe Attempt at a Solution
Do can not be greater than 2F...
I am stuck on this problem because it been like 6 yrs since i took geometry and its due by 9 am. please help!
Derive the thin lens equation:
1/object distance + 1/ image distance = 1/focal length
for a divergent lens, using a diagram of a divergent lens (hint: use similar triangles)...
I have to complete a chart using the thin lens forumla. Can someone please help me out? I know that the formula is 1/f= 1/do= 1/di, but I don't know how to use it.
Thanks.
A transparent photographic slide is placed in front of a converging lens with a focal length of 2.24 cm. The lens forms an image of the slide 11.4 cm from the slide.
(a) How far is the lens from the slide if the image is real?
(b) How far is the lens from the slide if the image is virtual...
Hi,
I'm first year Engineering in the Phys1130 course at my college and I've ended up hitting a large brick wall with the pre-lab. The pre-lab section of the experiment goes:
"The thin lens equation is:
(1/do) + (1/di) = (1/f)
di = distance from lens to image
do = distance from...