Refraction

What is Refraction of Light

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What is Refraction of Light

What is Refraction of Light
What is Refraction of Light 1
When a spoon is immersed into a glass of water, the spoon appears bent or broken as shown in Figure (a).
When a part of the word PHYSICS is covered with a glass slab as shown in Figure (b), the covered letters appear displaced.
The two situations described are perceptions due to the change of the direction of a light ray when it leaves the water or the glass and enters the air.

Refraction-of-light
Fig. Refraction of light from a plane transparent denser surface.

Definition: When light rays travelling in a medium are incident on a transparent surface of another medium they are bent as they travel in second medium.

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Some Associated Terms

  1. Transparent surface: The plane surface which refracts light, is called transparent surface. In diagram, XY is the section of a plane transparent surface.
  2. Point of incidence: The point on transparent surface, where the ray of light meets it, is called point of incidence. In diagram, Q is the point of incidence.
  3. Normal: Perpendicular drawn on the transparent surface at the point of incidence, is called normal. In diagram, N1QN2 is the normal on surface XY.
  4. Incident ray: The ray of light which strikes the transparent surface at the point of incidence, is called incident ray in diagram PQ is the incident ray.
  5. Refracted ray: The ray of light which travels from the point of incidence into the other medium, is called refracted ray. In diagram, QR is the refracted ray.
  6. Angle of incidence: The angle between the incident ray and the normal on the transparent surface at the point of incidence, is called the angle of incidence. It is represented by the symbol i. In diagram, angle PQN1 is the angle of incidence.
  7. Angle of refraction: The angle between the refracted ray and the normal on the transparent surface at the point of incidence, is called angle of refraction. It is represented by symbol r. In diagram angle RQN2 is the angle of refraction.
  8. Plane of incidence: The plane containing the normal and the incident ray, is called plane of incidence. For the diagram, plane of book page is the plane of incidence.
  9. Plane of refraction: The plane containing the normal and the refracted ray, is called plane of refraction. For the diagram, plane of book page is the plane of refraction.

Refraction of Light

What is Refraction of Light 2

  • Figure shows how light rays pass through a glass block. From the figure:
    • When a light ray (X) is incident normal (∠i = 0) to the boundary of the media (air to glass), it travels straight on without being bent.
    • When a light ray (Y) is incident at an acute angle to the boundary of the media, the light ray is bent or refracted.
    • The light ray bends towards the normal when it travels from a less dense medium (air) to a denser medium (glass).
    • The light ray bends away from the normal when it travels from a denser medium (glass) to a less dense medium (air).
    • The angle of refraction (∠r) is always smaller than the angle of incidence (∠i) when light travels from a less dense medium to a denser medium.
    • In the case of ray Y, the emergent ray is in the same direction as the incident ray but is laterally displaced. This is due to the two boundaries of the media, where the refractions occurred, being parallel to each other and that the refractions bend the ray equally and in opposite directions.
  • There is another interesting phenomenon which you can observe from Figure. At point A, ray Y travels from air to glass with an angle of incidence, i and an angle of refraction, r. At point B, ray Y travels from glass to air with an angle of incidence, r and an angle of refraction, i. It can be said that the ray, at point B, is travelling the exact same path as compared to point A, but in the opposite direction. This is the principle of reversibility of light.
  • Refraction of light is the bending of a light ray at the boundary as it travels from one medium to another.
  • Any substance that a light ray travels through is called a medium.
  • A medium, which is optically less dense or denser, has no connection with the formula,
    Density = Mass/Volume It is related only to the speed of light that travels through it. (All references to less dense and denser medium in this chapter is taken to mean optically less dense or denser.)
  • The more optically dense a medium is, the slower light travels through it.
  • A light ray travels much slower in a denser medium. When a light ray travels from one medium to another, its speed changes. The change in speed of the light ray causes it to change its direction.
  • The effect of refraction can also be explained by using the analogy of a car moving onto a sandy road as shown in Figure.
    What is Refraction of Light 3
  • As one of the front wheels of the car hits the sand, it slows down while the other wheel keeps going at its original speed. This will cause the direction of the car to change. The new direction of the car will be closer to the normal.

Laws of Refraction of Light

First Law:  The incident ray, the normal to the transparent surface at the point of incidence and the refracted ray, all lie in one and the same plane.
Second Law : The ratio of sine of angle of incidence to the sine of the angle of refraction is constant and is called refractive index of the second medium with respect to the first medium.
\(\frac{\text{sin i}}{\text{sin r}}=\text{ }\!\!\mu\!\!\text{ }\)

 

Analysing Refraction of Waves

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Analysing Refraction of Waves

  1. Figure shows a surfer approaching the beach. As the waves enter the shallow water near the beach, the wavelength of the waves decreases. Hence, the speed of the waves decreases as the water gets shallower.
    Analysing Refraction of Waves 1
  2. Refraction of waves is a phenomenon that occurs when there is a change of direction in the propagation of waves travelling from one medium to another due to a change of speed.
  3. The refraction of water waves occurs when water waves travel from one area to another area of different depths. Hence, the different depth of water is equivalent to a different medium.

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Characteristics of Refraction of Waves

Figure shows the refraction of water waves travelling from a deep area to a shallow area.
Analysing Refraction of Waves 2

  • Direction: The direction of the propagation of waves changed after refraction.
  • Angle of refraction: When waves propagate from a less dense medium to a denser medium, the angle of refraction is lesser than the angle of incidence.
  • Wavelength: The wavelength of the refracted waves in the denser medium is shorter (as in the case of water, shallower depth is equivalent to denser medium).
  • Frequency: The frequency of the waves remains unchanged.
  • Speed: The speed of the waves in the denser medium is less than that in the less dense medium.

Refraction of Plane Waves Experiment

Aim: To study the characteristics of refraction of plane waves in a ripple tank.
Material: White paper as screen
Apparatus: Ripple tank with its accessories, stroboscope, trapezium-shaped perspex plate, convex-shaped perspex plate, concave-shaped perspex plate
Method:

Refraction of Plane Waves Experiment 1       Refraction of Plane Waves Experiment 2

  1. The ripple tank is arranged as shown in Figure.
  2. The legs of the ripple tank are adjusted so that the base of the tank is horizontal. The tank is filled with water.
  3. A trapezium-shaped perspex plate is placed in the tank to create a shallow area as shown in Figure.
    Refraction of Plane Waves Experiment 3
  4. A horizontal vibrating beam is used to create plane (straight) waves.
  5. The speed of the motor is adjusted to produce a train of waves that can be clearly observed on the screen with the help of a stroboscope.
  6. The position of the perspex plate is adjusted with its edge parallel and then at an angle with the vibrating beam. For each case, the wavefronts at the deep and shallow areas of the tank are observed.
  7. The trapezium-shaped perspex plate is replaced with the convex-shaped perspex plate and then with the concave-shaped perspex plate. For each case, the wavefronts are observed at the deep and shallow areas of the tank.

Observations:
Refraction of Plane Waves Experiment 4
Refraction of Plane Waves Experiment 5
Refraction of Plane Waves Experiment 6
Refraction of Plane Waves Experiment 7The above Figures show the observed wavefronts for the respective perspex plates.
Discussion:

  1. When water waves travel from a deep area to a shallow area as in Figure, the direction of the waves is refracted towards the normal.
    Refraction of Plane Waves Experiment 8
  2. Therefore, the angle of incidence, i of the water waves is greater than the angle of refraction, r.
  3. When water waves travel from an area into another of different depths, their speeds vary. The frequency of the waves which is equal to the frequency of the motor remains unchanged.
  4. Figure shows plane water waves travelling from a deep area to a shallow area. Using the formula v = fλ, where vd = fλd and vs = fλs, f remains unchanged. Since λd > λs, therefore, vd > vs The wave speed at the deep area, vd is greater than the wave speed at the shallow area, vs.

Refraction of Plane Waves Experiment 9

Refraction of Light Experiment

Aim: To study the characteristics of refraction of light.
Material: White paper
Apparatus: Glass block, ray box, power supply, protractor
Method:

Refraction of Plane Waves Experiment 10

  1. The apparatus is set up as shown in Figure.
  2. A ray of light is directed at an angle of incidence, i = 300 to the glass block.
  3. The ray that enters the glass block is observed and the angle of refraction, r is measured.
  4. Steps 2 and 3 are repeated for angles of incidence, i = 450 600 and 750.

Observation:
It is observed that when a light ray travels from air into the g ass block, it is refracted towards the normal.
Refraction of Plane Waves Experiment 11Discussion:

  1. Glass is a denser medium than air. A light ray travels at a slower speed in glass compared with in air.
  2. When a light ray travels from a less dense medium to a denser medium and the ang e of incidence, i is not zero, then the angle of incidence, i is greater than the angle of refraction, r.

Refraction of Sound Waves Experiment

Aim: To study the characteristics of refraction of sound waves.
Material: Balloon filled with carbon dioxide
Apparatus: Audio signal generator, loudspeaker, microphone, cathode ray oscilloscope (C.R.O.)
Method:

Refraction of Plane Waves Experiment 12

  1. The apparatus is set up as shown in Figure.
  2. The C.R.O. settings are adjusted to detect the sound waves emitted from the loudspeaker.
  3. The position of the microphone is adjusted by moving it nearer to the balloon or further away from it until the biggest amplitude of the waves is displayed on the screen.
  4. The balloon is removed as shown in Figure and the amplitude of the trace displayed on the screen is observed and compared with that observed in step 3.
    Refraction of Plane Waves Experiment 13

Observation:

  1. In step 3, the amplitude of the trace displayed on the screen is bigger than that in step 4.
  2. This shows that a louder sound is detected when a balloon is placed between the loudspeaker and the microphone.

Discussion:

  1. When the screen of the C.R.O. displays a trace of bigger amplitude for a sound wave, it indicates a louder sound is detected. This shows that the balloon which is filled with carbon dioxide has focused the sound waves emitted from the loudspeaker to the microphone.
  2. From the observation, the sound waves that travel through ordinary atmospheric air (less dense medium) to carbon dioxide (denser medium) undergo refraction.

Image Formation by Concave and Convex Lenses

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Image Formation By Convex Lens in Different Cases

Case 1: Object at Infinity
A point object lying on the principal axis:
Rays come parallel to the principal axis and after refraction from the lens, actually meet at the second principal focus F2.
Image-Formation-By-Concave-And-Convex-Lenses-1
Fig. Convex lens point object at infinity, image at focus.
The image is formed at focus F2. It is real and point sized.

A big size object with its foot on the principal axis:
Parallel rays come inclined to the principal axis. Image of foot is formed at the focus.
Image is formed at the second principal focus F2. It is real inverted and diminished (smaller in size than the object). (Fig.)
Parallel rays from infinity
Image-Formation-By-Concave-And-Convex-Lenses-2
Fig. Convex lens : big size object at infinity, image at focus

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Case 2: Object at distance more than twice the Focal Length
Real object AB has its image A’B’ formed between distance f and 2f.
The image is real inverted and diminished (smaller in size than the object)
Image-Formation-By-Concave-And-Convex-Lenses-3
Fig. Convex lens : object beyond 2f, image between f and 2f.

Case 3: Object at distance twice the Focal Lengths
Real object AB has its image A’B’ formed at distance 2f.
Image-Formation-By-Concave-And-Convex-Lenses-4
Fig. Convex lens : object at distance 2f, image at distance 2f.
The image is real, inverted and has same size as the object.

Case 4: Object at distance more than Focal Length and less than twice is Focal Length
Real object AB has its image A’B’ formed beyond distance 2f.
Image-Formation-By-Concave-And-Convex-Lenses-5
Fig. Convex lens : object at distance between f and 2f, image beyond 2f.
The image is real inverted and enlarged (bigger in size than the object).

Case 5: Object at Focus
Real object AB has its image formed at infinity.
Image-Formation-By-Concave-And-Convex-Lenses-6
Fig. Convex lens : object at focus, image at infinity.
The image is imaginary inverted (refracted rays to downward) and must have very large size.

Case 6: Object between Focus and Optical Centre
Real object AB has its image A’B’ formed in front of the lens.
Image-Formation-By-Concave-And-Convex-Lenses-7

Image Formation By Concave Lens in Different Cases

Case 1: Object at infinity
A point object lying on the principal axis:
Rays come parallel to the principal axis and after refraction from the lens, appears to come from the second principal focus F2.
Image-Formation-By-Concave-And-Convex-Lenses-9
Fig. Concave lens point object at infinity, image at focus.
The image is formed at focus F2. It is virtual and point sized (fig.)

A big size object with its foot on the principal axis:
Parallel rays come inclined to the principal axis. Image of foot is formed at focus.
The image is formed at the second principal focus F2.
It is virtual–erect and diminished (fig.)
Image-Formation-By-Concave-And-Convex-Lenses-10
Fig. Concave lens : big size object at infinity image at focus.

Case 2: Object at a Finite Distance
Real object AB has its image A’B’ formed between second principal focus F2 optical centre C.
The image is virtual–erect and diminished.