# Geometric optics Definition and 29 Discussions

Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of rays. The ray in geometric optics is an abstraction useful for approximating the paths along which light propagates under certain circumstances.
The simplifying assumptions of geometrical optics include that light rays:

propagate in straight-line paths as they travel in a homogeneous medium
bend, and in particular circumstances may split in two, at the interface between two dissimilar media
follow curved paths in a medium in which the refractive index changes
may be absorbed or reflected.Geometrical optics does not account for certain optical effects such as diffraction and interference. This simplification is useful in practice; it is an excellent approximation when the wavelength is small compared to the size of structures with which the light interacts. The techniques are particularly useful in describing geometrical aspects of imaging, including optical aberrations.

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1. ### Evaluate the outgoing radiation from an optical fiber on a surface

The geometric configuration that I am adopting is the following, I hope you understand. The optical fiber is positioned relative to the bottom surface at a height ##a## and an angle ##\alpha## with respect to the y-axis in the yz-plane with x = 0. ##b## is the distance between the origin and...
2. ### Apparent depth of an object underwater

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##...
3. ### Image position and magnification for underwater spherical lens

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...
4. ### I Applications of Virtual objects

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...
5. ### How do you know if the focal length is positive or negative?

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?
6. ### Geometrical optics: using Snell's law, find the depth of the pool

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
7. ### I What does "upright" mean in geometric optics?

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 .
8. ### A reflective spherical balloon

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
9. ### Position of the image of an object placed in water

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...
10. ### Light incident on a sphere, focused at a distance ##2R##

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...
11. ### Combination of thin lens and concave mirror

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...
12. ### Size of a fish under water

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.
13. ### Inserting thick lenses into a thin lens system and deducing values

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...
14. ### Jenkins-White Optics: Relation between Prism/Deviation Angle and Rays

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...
15. ### B What does coefficient of increase of physical quantity mean?

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...
16. ### An analytic expression to describe spherical aberration

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...
17. ### Real image appears in front of the mirror?

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...
18. ### Length of the shadow

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...
19. ### Is the equivalent lens of two such that f_1+f_2<h divergent?

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...
20. ### Ray diagram diverging lens both object and image virtual

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 Equations The Attempt at a Solution I did not find this particular case of ray diagram in any textbook so I would like to know...
21. ### Compound lens separated by a distance

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: $$\frac{1}{s} +\frac{1}{s'}=\frac{1}{f_1}$$...
22. ### Radius of Curvature to Correct Myopia

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...
23. ### Image of a virtual object by a plane mirror

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...
24. ### Measurement of Focal length with Laser beam

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...
25. ### Fermat's Principle to explain lenses and mirrors

How do we use Fermat's principle of least time to explain the required shapes of lenses and mirrors?
26. ### Question about lens maker's formula

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 [Broken]) I can understand the first equation because it is just the object–image relationship for...
27. ### Refraction through an optical fiber

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...
28. ### Vessel with liquids having different refractive index

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...
29. ### Hand drawn ray tracing through an optical system

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...