Geometric optics Definition and 76 Threads

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height...

I'm often confused about when it's appropriate to use geometric optics (ray tracing) and when it's necessary to switch to wave optics and analyze the wavefront instead. For example, in many interference problems, the conclusions derived from ray tracing are often correct—even though...

Hello all, I am facing challenges in coupling light from a very small source, 1 mm in size, into a spectrometer. The spectrometer is about 660 mm long, Czerny-Turner geometry, with grating size about 55 mm. The challenge is to record a spatially resolved spectrum with a 2D (about 1000x1000...

Hello , I study the principles of optical coherence tomography, where we emit light and by the refraction that we detect we reconstruct and image, but I don't understand why we use low coherence light , if i want to measure the refracted light i would prefer to have coherent light so that the...

I would know how to solve this problem if the person had been standing pratically above of the object underwater by using Snell's law and the approximation ##\sin(\theta)\approx\tan(\theta)## fopr ##\theta## small, but in this case I don't see how to find the angles ##\theta_1## and ##\theta_2##...

Using the data given and recalling that in this configuration ##R<0## I get: ##\frac{1.33}{0.5}+\frac{1.5}{q}=\frac{1.5-1.33}{-0.2}\Rightarrow q\approx -0.427 m=-42.7 cm## so the image is virtual and is ##42.7\ cm## to the left of vertex ##V##. The magnification is ##M=\frac{n_1 q}{n_2...

I've heard virtual objects are used in cinema halls I'm not sure of what that means, can someone explain this to me please? And btw by virtual object i mean when diverging rays from real object passes through a convex lens, the rays will converging and if you'll place a plane mirror infront of...

In this problem, it doesn't tell you where is the focal length. So how do you know if it is in front or behind the object?

α=30°; l=0.5 m; n1=1; n2=1.33 α+β=90°, so β=90°-30°=60°. Using Snell's law: sinβ/sinγ = n2/n1 sinγ≈0.651 γ≈41°. β=γ+θ (vertical angles) θ=60°-41°=19° tan(θ+β)=l/h h=l/tan(θ+γ) h=0.5/(tan(19+41))≈0.289 m

if someone want to explain to me what is an upright image ? , and what are the other adjectives to define an image in geometric optics and their meaning , Thanks .

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 tried using the formula for the refraction of a spherical lens ##\frac{n_1}{p}+\frac{n_2}{q}=\frac{n_2-n_1}{R}## consider each slab as a spherical lens with curvature ##R=\infty## and by doing that I get ##\frac{1.33}{10}+\frac{1.5}{q}=0\Leftrightarrow q\approx -11.3 cm##. Since the piece of...

I used the equation for the refraction on a spherical surface: ##\frac{n_1}{p}+\frac{n_2}{q}=\frac{n_2-n_1}{R}##, where ##n_1=1## is the index of refraction of air, ##n_2## the index of refraction of the sphere, ##R## is the radius of the glass sphere, ##p## is the object distance which, since...

At the start of this section §22.5 (Geometric Optics in curved Spacetime), the amplitude of the vector potential is given as: A = ##\mathfrak R\{Amplitude \ X \ e^{i\theta}\} ## The Amplitude is then re=expressed a "two-length-scale" expansion (fine!) but it then is modified further to...

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...

From This picture, I think the fish will be smaller but the problem is how small will it be? (Fish "L" is the image of fish "K") Let ##H## be the depth of fish "K", ##\theta## be the angle of eyes to y-axis and ##n## is the index of refraction of water.

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've tried to attempt the first part of the problem(spent over an hour on this) as second part could be easily optained with some calculus ,I asked my friend but alas nobody could conjure the solution to this dangerous trigonometric spell. It was just pages and pages of concoction of...

Homework Statement A 2.0-cm-tall candle flame is 2.0 m from a wall. You happen to have a lens with a focal length of 32 cm. How many places can you put the lens to form a well-focused image of the candle flame on the wall? For each location, what are the height and orientation of the image...

How is the "geometric optics approximation" exactly defined? Given all the source of visible radiation's parameters, all the apparatus, instruments, screen, etc, specifications, how can I know if, e. g. there will be diffraction, interference or other wave properties or if I'll be able to...

I am extremely confused by the use of the term coefficient of increase of something. For example , if it is stated that the index of refraction varies linearly with a coefficient of 2.5×10^-5, how is this coefficient defined? Is it simply the slope of the line plotted with index of refraction on...

Homework Statement Derive an analytic expression for the distance from the vertex to the focus for a particular ray in terms of (i) the radius of curvature R of the concave mirror (ii) the angle of incidence θ between incident ray and radius of the mirror. Hence show that the focus moves closer...

Is there a simple way to determine or prove this? Real images are always inverted, and unlike virtual images can be projected onto a screen (I'm not even sure what this means to be honest). If I look at the back end of a spoon (convex mirror), the image is always upright and therefore virtual...

Homework Statement At the outside, there is a vertical stick with a length of 1.1 meter and its shadow on the surface of an Earth is 1.3 meter, there also is light pole and its shadow length is 5.2 meters, what is the height of that light pole? Homework Equations Trigonometry equations to...

Homework Statement A person with a near point of 100 cm , but excellent distant vision, normally wears corrective glasses. But he loses them while traveling. Fortunately, he has his old pair as a spare. If the lenses of the old pair have a power of +2.55 diopters , what is his near point...

The focal of the lens equivalent of two thin lens at distance h is $$1/f=1/f_1+1/f_2+h/(f_1 f_2)$$ Therefore, supposing that ##f_1>0## and ##f_2>0## (both lenses are convergent), if ##f_1+f_2 <h## then the equivalent lens should be divergent. Nevertheless consider the example in picture...

Homework Statement Draw the ray diagram of the case of a diverging lens where both object and image are virtual, that is ##f<0## , ##p<0## with ##p<f## Homework EquationsThe Attempt at a Solution I did not find this particular case of ray diagram in any textbook so I would like to know where...

Homework Statement A farsighted boy has a near point at 2.3 m and requires eyeglasses to correct his vision. Corrective lenses are available in increments in power of 0.25 diopters. The eyeglasses should have lenses of the lowest power for which the near point is no further than 25 cm. The...

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 A person's eye has a near point of 7 cm. The cornea at the outer surface of the eye has a refractive index of n_c = 1.376 and forms a convex shape with a radius of curvature of R_2 = 8 mm against air. The figure below shows the same eye with a contact lens (refractive index...

A plane mirror forms a virtual image of a real object placed in front of it and a real image of a virtual object placed in front of it. I can't picture the second case. Please show me a ray diagram showing real image formation by a plane mirror or just explain the case of real image formation by...

Homework Statement Background from previous parts of the question: A simple isotropic dielectric occupies the region x>0, with vacuum in region x<0. I've found the wave equations for the electric field Incident, reflected and transmitted to prove Snell's law (Sinθ/Sinθ = c/c' = √εr) and the law...

Homework Statement Hi! I have lately come across some tricky experimental physics tasks, where no solution is given. Some of them involved parts where the focal length of a convex lens had to be measured with a laser. How do you do this? Homework Equations 1/l + 1/d = 1/f (1) where f is the...

Homework Statement A ray travels as shown in the image attached below. In this case, Fermat's principle may be written as ##A =\frac{n(1+ay)}{\sqrt{1+(y')^2}}## Where y' is dy/dx, n is the index of refraction and A is a real constant. The trajectory of a ray of light is given by ##y =...

How do we use Fermat's principle of least time to explain the required shapes of lenses and mirrors?

guys i want a book where i can find questions on geometric optics especially for questions based on locating position of mirror by ray diagram when only object and image are given? I have already found 2 questions in I.E. Irodov but i want more so please suggest other books..... thnx

a concave mirror of 5cm radius of curvature whose circular ring has a radius of 4cm is blackened except for a narrow strip round the edge. A beam of light parallel to the principal axis falls on the mirror. Find the distance between the centre of curvature of mirror and the point at which light...

I am trying to follow the derivation of lens maker's formula from the textbook "University Physics", p.1133 (https://books.google.com.hk/books?id=nQZyAgAAQBAJ&pg=PA1133#v=onepage&q&f=false ) I can understand the first equation because it is just the object–image relationship for spherical...

Homework Statement A fish 2cm long is floating in a spherical glass fishtank with radius 20cm. The glass is 0.8cm thick and has index of refraction n=1.56. The index of refraction of water is 1.33. Find the apparent position and length of the fish. Homework EquationsThe Attempt at a Solution I...

I can't seem to find the proof for the distance between the two parallel lines. Homework Equations : Snells law: μ1sinθ1=μ2sinθ2 Sin (A+B)= sinAcosB + sinBcosA[/B]The Attempt at a Solution : tried using the parallel lines to get a result in terms of the initial angle of incidence ϑ, as the...

Homework Statement Given a "new type" of optical fiber (index of refraction n = 1.23), a laser beam is incident on the flat end of a straight fiber in air. Assume nair = 1.00. What is the maximum angle of incidence Ø1 if the beam is not to escape from the fiber? (See attached file for...

1.Problem: A vessel is quarter filled with a liquid of refractive index A. the remaining parts of the vessel is filled with an immiscible liquid of refractive index 3A/2. The apparent depth of the vessel is 50% of the actual depth. the value of A is? 1)1 2)3/2 3)2/3 4)4/3 Solution: 1...

Homework Statement First, thanks in advace. Let us consider a microscope where the objective L1 has f1=20mm and magnification 10x. In the image plane is located a diafragm M with diameter 19mm (see fig). The size of the CCD is 4,8mm (vertical) x 5,6mm (horizontal). 20mm before of the CCD...

Hi, I am familiar with drawing rays through a lens. But when a few lenses are put together, things become confusing to me. For example, if a first positive thin lens at 0 forms a real image 10cm away, what would happen when we put a second positive thin lens, say at 5cm along the optical...

Homework Statement A concave mirror forms an image on a screen twice as large as an object. Both object and mirror are then moved such that the new image is 3x the size of the object. If the screen is moved 75cm, how far did the object move? Homework Equations m = image distance / object...

Homework Statement Explain the physical principle of total internal reflection used by optical cables. Calculate the critical angle of incidence that corresponds to a refracted angle θair = 90 Next, calculate the critical angle for a bare glass fiber submerged in water nH2O = 1.33...

Homework Statement A ray is deflected by 2.37cm by a piece of acrylic. Find the thickness t of the acrylic if the incident angle is 50.5 degrees. http://imgur.com/kx2VT5c Homework Equations n1sinΘ1 = n2sinΘ2 The Attempt at a Solution n of acrylic is 1.5. Therefore, the refracted...

Why is the position of an image the intersection of 2+ rays?

An infinity corrected microscope objective has a magnification of 100× for a tube lens with focal length 180 mm. The numerical aperture of the objective is 0.90. Calculate the the diffraction limited spatial resolution if the objective is used with red light (660 nm). (Ans.: f=1.8 mm; d=447...

Homework Statement An object is placed 400 mm in front of a convex lens of focal length 80 mm. Find the position of the image formed. State the nature of this image. A second convex lens of magnifying power X8 is placed 125 mm behind the first convex lens. What is the focal length of...