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By the end of this section, you will be able to:
  • Describe image formation by a single refracting surface
  • Determine the location of an image and calculate its properties by using a ray diagram
  • Determine the location of an image and calculate its properties by using the equation for a single refracting surface

When rays of light propagate from one medium to another, these rays undergo refraction, which is when light waves are bent at the interface between two media. The refracting surface can form an image in a similar fashion to a reflecting surface, except that the law of refraction (Snell’s law) is at the heart of the process instead of the law of reflection.

Refraction at a plane interface—apparent depth

If you look at a straight rod partially submerged in water, it appears to bend at the surface ( [link] ). The reason behind this curious effect is that the image of the rod inside the water forms a little closer to the surface than the actual position of the rod, so it does not line up with the part of the rod that is above the water. The same phenomenon explains why a fish in water appears to be closer to the surface than it actually is.

Figure depicts the side view of a rod dipped in water. A lighter line labeled image of rod is shown in such a way that it appears as if the rod is bent at the junction of air and water. Point P is on the rod and point Q is on the image of rod. A dotted line PQ is shown perpendicular to the surface of the water. Two rays originate from P, travel upwards to the surface of the water, bend at an angle and reach the eye of the observer. The back extensions of the bent rays seem to originate from point Q.
Bending of a rod at a water-air interface. Point P on the rod appears to be at point Q , which is where the image of point P forms due to refraction at the air-water interface.

To study image formation as a result of refraction, consider the following questions:

  1. What happens to the rays of light when they enter or pass through a different medium?
  2. Do the refracted rays originating from a single point meet at some point or diverge away from each other?

To be concrete, we consider a simple system consisting of two media separated by a plane interface ( [link] ). The object is in one medium and the observer is in the other. For instance, when you look at a fish from above the water surface, the fish is in medium 1 (the water) with refractive index 1.33, and your eye is in medium 2 (the air) with refractive index 1.00, and the surface of the water is the interface. The depth that you “see” is the image height h i and is called the apparent depth    . The actual depth of the fish is the object height h o .

Figure shows the side view of some quantity of water. Point P lies within it. Two rays originate from point P, bend at the surface of the water and reach the eye of the observer. The back extensions of these refracted rays intersect at point Q. PQ is perpendicular to the surface of the water and intersects it at point O. Distance OP is labeled h subscript o and distance OQ is labeled h subscript i. The angle formed by the refracted ray with a line perpendicular to the surface of the water is labeled theta.
Apparent depth due to refraction. The real object at point P creates an image at point Q . The image is not at the same depth as the object, so the observer sees the image at an “apparent depth.”

The apparent depth h i depends on the angle at which you view the image. For a view from above (the so-called “normal” view), we can approximate the refraction angle θ to be small, and replace sin θ in Snell’s law by tan θ . With this approximation, you can use the triangles Δ O P R and Δ O Q R to show that the apparent depth is given by

h i = ( n 2 n 1 ) h o .

The derivation of this result is left as an exercise. Thus, a fish appears at 3/4 of the real depth when viewed from above.

Refraction at a spherical interface

Spherical shapes play an important role in optics primarily because high-quality spherical shapes are far easier to manufacture than other curved surfaces. To study refraction at a single spherical surface, we assume that the medium with the spherical surface at one end continues indefinitely (a “semi-infinite” medium).

Questions & Answers

how those weight effect a stable motion at equilibrium
Nonso Reply
how do I differentiate this equation- A sinwt with respect to t
Evans Reply
just use the chain rule : let u =wt , the dy/dt = dy/du × du/dt : wA × cos(wt)
Jerry
I see my message got garbled , anyway use the chain rule with u= wt , etc...
Jerry
de broglie wave equation
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vy beautiful equation
chandrasekhar
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fitsum Reply
when you consider systems consisting of fixed charges
Sherly
Diagram of the derive rotational analog equation of v= u+at
Nnamnso Reply
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Arnulfo Reply
a unit of weight for precious stones and pearls, now equivalent to 200 milligrams.
LoNE
a science that deals with the composition, structure, and properties of substances and with the transformations that they undergo.
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Mrs Reply
what chemistry ?
Abakar
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Fred Reply
ok
Giorgi
acids and bases
Navya
How does unpolarized light have electric vector randomly oriented in all directions.
Tanishq Reply
unpolarized light refers to a wave collection which has an equal distribution of electric field orientations for all directions
pro
In a grating, the angle of diffraction for second order maximum is 30°.When light of wavelength 5*10^-10cm is used. Calculate the number of lines per cm of the grating.
Micheal Reply
OK I can solve that for you using Bragg's equation 2dsin0over lander
ossy
state the law of gravity 6
cletus Reply
what is cathodic protection
Ebe Reply
its just a technique used for the protection of a metal from corrosion by making it cathode of an electrochemical cell.
akif
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Sonu Reply
what is interferometer
Abakar
Show that n1Sino1=n2Sino2
javan Reply
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Vikas Reply
is it in context of waves?
Edgar
It is the manner of motion of the energy whether mechanical(requiring elastic medium)or electromagnetic(non interference with medium)
Edgar
Practice Key Terms 3

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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