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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 does colour appear in thin films
Nwjwr Reply
in the wave equation y=Asin(kx-wt+¢) what does k and w stand for.
Kimani Reply
derivation of lateral shieft
James Reply
Hi
Amjad
Hi
Amjad
hi
ALFRED
how are you?
Amjad
hi
asif
hi
Imran
I'm fine
ALFRED
total binding energy of ionic crystal at equilibrium is
All Reply
How does, ray of light coming form focus, behaves in concave mirror after refraction?
Bishesh Reply
Refraction does not occur in concave mirror. If refraction occurs then I don't know about this.
Sushant
What is motion
Izevbogie Reply
Anything which changes itself with respect to time or surrounding
Sushant
good
Chemist
and what's time? is time everywhere same
Chemist
No
Sushant
how can u say that
Chemist
do u know about black hole
Chemist
Not so more
Sushant
Radioactive substance
DHEERAJ
These substance create harmful radiation like alpha particle radiation, beta particle radiation, gamma particle radiation
Sushant
But ask anything changes itself with respect to time or surrounding A Not any harmful radiation
DHEERAJ
explain cavendish experiment to determine the value of gravitational concept.
Celine Reply
For the question about the scuba instructor's head above the pool, how did you arrive at this answer? What is the process?
Evan Reply
as a free falling object increases speed what is happening to the acceleration
Success Reply
of course g is constant
Alwielland
acceleration also inc
Usman
which paper will be subjective and which one objective
jay
normal distributiin of errors report
Dennis
normal distribution of errors
Dennis
acceleration also increases
Jay
there are two correct answers depending on whether air resistance is considered. none of those answers have acceleration increasing.
Michael
Acceleration is the change in velocity over time, hence it's the derivative of the velocity with respect to time. So this case would depend on the velocity. More specifically the change in velocity in the system.
Big
photo electrons doesn't emmit when electrons are free to move on surface of metal why?
Rafi Reply
What would be the minimum work function of a metal have to be for visible light(400-700)nm to ejected photoelectrons?
Mohammed Reply
give any fix value to wave length
Rafi
40 cm into change mm
Arhaan Reply
40cm=40.0×10^-2m =400.0×10^-3m =400mm. that cap(^) I have used above is to the power.
Prema
i.e. 10to the power -2 in the first line and 10 to the power -3 in the the second line.
Prema
there is mistake in my first msg correction is 40cm=40.0×10^-2m =400.0×10^-3m =400mm. sorry for the mistake friends.
Prema
40cm=40.0×10^-2m =400.0×10^-3m =400mm.
Prema
this msg is out of mistake. sorry friends​.
Prema
what is physics?
sisay Reply
why we have physics
Anil Reply
because is the study of mater and natural world
John
because physics is nature. it explains the laws of nature. some laws already discovered. some laws yet to be discovered.
Yoblaze
physics is the study of non living things if we added it with biology it becomes biophysics and bio is the study of living things tell me please what is this?
tahreem
physics is the study of matter,energy and their interactions
Buvanes
all living things are matter
Buvanes
why rolling friction is less than sliding friction
tahreem
thanks buvanas
tahreem
is this a physics forum
Physics Reply
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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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