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Karnataka Board PUCPUC Science 2nd PUC Class 12
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Refraction of a Plane Wave

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Estimated time: 5 minutes
CBSE: Class 12

Refraction of a Plane Wave

We can similarly use Huygens principle to derive the laws of refraction.

Consider a plane wavefront AB incident in the direction shown in Fig. on the interface PP' separating two media 1 and 2, as shown. Let the speed of light be v1​ in medium 1 and v2​ in medium 2. We assume that the medium 2 is denser than medium 1. When the wavefront AB advances, point A reaches the interface first and then point B reaches the interface after some time. During this time, the secondary wavelet from A travels a distance AE equal to v2τ is the time taken by the point B to reach the interface from C to B. In the same time τ, the point B reaches from C to B in medium 1 and the distance covered is

BC = v1τ

As before, draw a tangent CE to the secondary wavelet from A. The refracted wavefront is CE and the refracted ray is the normal to this wavefront.

CBSE: Class 12

Geometry of Refraction

From Fig. we have

sin⁡ i = \[\frac {BC}{AC}\]

and

sin ⁡r = \[\frac {AE}{AC}\]​

Therefore,

\[\frac{\sin i}{\sin r}=\frac{BC}{AE}=\frac{v_1\tau}{v_2\tau}=\frac{v_1}{v_2}\]
CBSE: Class 12

Refractive Indices

If n1​ is the refractive index of medium 1 and n2​ that of medium 2, then,

\[\frac{\sin i}{\sin r}=\frac{v_1}{v_2}=\frac{n_2}{n_1}\]

or,

n1sin⁡ i = n2sin⁡ r

This is Snell's law of refraction.

CBSE: Class 12

Wavelength and Frequency on Refraction

From the above discussion, it follows that when a light wave travels from one medium to another, its speed changes but its frequency remains the same. Therefore, if λ1​ and λ2​ are the wavelengths of light in the two media,

λ1 = \[\frac {v_1}{ν}\], λ2 = \[\frac {v_2}{ν}\]

Therefore,

\[\frac {λ_1}{λ_2}\] = \[\frac {v_1}{v_2}\]

Thus, the wavelength of light decreases when it goes from a rarer to a denser medium.

It is interesting to see that although the ray picture of light allowed us to explain reflection and refraction, it was silent on the question as to why the speed of light should be greater in one medium than the other. To answer this question, we had to resort to the wave picture of light. And when we do that, we see that the speed of light in the denser medium is lower than that in the rarer medium. This is exactly the opposite of what was deduced from the particle picture of light.

Related QuestionsVIEW ALL [11]

Let us list some of the factors, which could possibly influence the speed of wave propagation:

(i) Nature of the source

(ii) Direction of propagation

(iii) Motion of the source and/or observer

(iv) Wavelength

(v) Intensity of the wave

On which of these factors, if any, does the speed of light in vacuum?

The optical properties of a medium are governed by the relative permittivity (εr) and relative permeability (µr). The refractive index is defined as `sqrt(µ_r ε_r) = n`. For ordinary material εr > 0 and µr > 0 and the positive sign is taken for the square root. In 1964, a Russian scientist V. Veselago postulated the existence of material with εr < 0 and µr < 0. Since then such ‘metamaterials’ have been produced in the laboratories and their optical properties studied. For such materials `n = - sqrt(µ_r ε_r)`. As light enters a medium of such refractive index the phases travel away from the direction of propagation.

  1. According to the description above show that if rays of light enter such a medium from air (refractive index = 1) at an angle θ in 2nd quadrant, them the refracted beam is in the 3rd quadrant.
  2. Prove that Snell’s law holds for such a medium.

Explain how Corpuscular theory predicts the speed of light in a medium, say, water, to be greater than the speed of light in vacuum. Is the prediction confirmed by experimental determination of the speed of light in water? If not, which alternative picture of light is consistent with the experiment?

A light ray in a medium (RI = 5/3) enters another medium at an angle of 30°. The angle in the other medium is sin-1 (5/6). The incident angle must be increased such that the ray is completely reflected at minimum degrees is ______.

The refractive index of glass is 1.5. What is the speed of light in glass? (Speed of light in vacuum is 3.0 × 108 m s−1)

Using Huygens’s construction of secondary wavelets draw a diagram showing the passage of a plane wavefront from a denser to a rarer medium. Using it verifies Snell’s law.

The wavefronts of a light wave travelling in vacuum are given by x + y + z = c. The angle made by the direction of propagation of light with the X-axis is _________ .

Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism?

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