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state laws of refraction

Law of Refraction

The law of refraction, which is generally known as Snell's law, governs the behaviour of light-rays as they propagate across a sharp interface between two transparent dielectric media.

Consider a light-ray incident on a plane interface between two transparent dielectric media, labelled 1 and 2, as shown in Fig. 57. The law of refraction states that the incident ray, the refracted ray, and the normal to the interface, all lie in the same plane. Furthermore, 

begin{displaymath}nn_1,sintheta_1 = n_2,sintheta_2,nend{displaymath}(341)

 

where $theta_1$ is the angle subtended between the incident ray and the normal to the interface, and $theta_2$ is the angle subtended between the refracted ray and the normal to the interface. The quantities $n_1$ and $n_2$ are termed the refractive indices of media 1 and 2, respectively. Thus, the law of refraction predicts that a light-ray always deviates more towards the normal in the optically denser medium: i.e., the medium with the higher refractive index. Note that $n_2>n_1$ in the figure. The law of refraction also holds for non-planar interfaces, provided that the normal to the interface at any given point is understood to be the normal to the local tangent plane of the interface at that point.

Figure 57: The law of refraction.
begin{figure}nepsfysize =3inncenterline{epsffile{refract.eps}}nend{figure}

 

By definition, the refractive index $n$ of a dielectric medium of dielectric constant $K$ is given by 

begin{displaymath}nn = sqrt{K}.nend{displaymath}(342)

 

Table 4 shows the refractive indices of some common materials (for yellow light of wavelength $lambda =589$nm). 

 

Table 4: Refractive indices of some common materials at $lambda =589$nm.
Material$n$
Air (STP)1.00029
Water1.33
Ice1.31
Glass: 
 Light flint1.58
 Heavy flint1.65
 Heaviest flint1.89
Diamond2.42

 

 

The law of refraction follows directly from the fact that the speed $v$ with which light propagates through a dielectric medium is inversely proportional to the refractive index of the medium (see Sect. 11.3). In fact, 

begin{displaymath}nv =frac{c}{n},nend{displaymath}(343)

 

where $c$ is the speed of light in a vacuum. Consider two parallel light-rays, $a$ and $b$, incident at an angle $theta_1$ with respect to the normal to the interface between two dielectric media, 1 and 2. Let the refractive indices of the two media be $n_1$ and $n_2$ respectively, with $n_2>n_1$. It is clear from Fig. 58 that ray $b$ must move from point $B$ to point $Q$, in medium 1, in the same time interval, ${mitDelta} t$, in which ray $a$ moves between points $A$ and $P$, in medium 2. Now, the speed of light in medium 1 is $v_1=c/n_1$, whereas the speed of light in medium 2 is $v_2=c/n_2$. It follows that the length $BQ$ is given by $v_1,{mitDelta} t$, whereas the length $AP$ is given by $v_2,{mitDelta} t$. By trigonometry, 

begin{displaymath}nsintheta_1 = frac{BQ}{AQ} = frac{v_1,{mitDelta} t}{AQ},nend{displaymath}(344)

 

and 

begin{displaymath}nsintheta_2 = frac{AP}{AQ} = frac{ v_2,{mitDelta} t}{AQ}.nend{displaymath}(345)

 

Hence, 

begin{displaymath}nfrac{sintheta_1}{sintheta_2} = frac{v_1}{v_2} = frac{n_2}{n_1},nend{displaymath}(346)

 

which can be rearranged to give Snell's law. Note that the lines $AB$ and $PQ$ represent wave-fronts in media 1 and 2, respectively, and, therefore, cross rays $a$ and $b$ at right-angles.

Figure 58: Derivation of Snell's law.
begin{figure}nepsfysize =3.5inncenterline{epsffile{diagram.eps}}nend{figure}

 

When light passes from one dielectric medium to another its velocity $v$ changes, but its frequency $f$ remains unchanged. Since, $v=f,lambda$ for all waves, where $lambda$ is the wavelength, it follows that the wavelength of light must also change as it crosses an interface between two different media. Suppose that light propagates from medium 1 to medium 2. Let $n_1$ and $n_2$ be the refractive indices of the two media, respectively. The ratio of the wave-lengths in the two media is given by 

begin{displaymath}nfrac{lambda_2}{lambda_1} = frac{v_2/f}{v_1/f} =nfrac{v_2}{v_1}=frac{n_1}{n_2}.nend{displaymath}(347)

 

Thus, as light moves from air to glass its wavelength decreases.

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The Laws of Refraction

  1. Incident ray, reflected ray, refracted ray and the normal of the system lie in the same plane.
  2. Incident ray, coming from one medium to the boundary of another medium, is refracted with a rule derived from a physicist Willebrord Snellius. He found that there is a constant relation between the angle of incident ray and angle of refracted ray. This constant is the refractive index of second medium relative to the first medium. He gives the final form of this equation like;

 

law of refraction

 

 



Where n1 is the refractive index of first medium and n2 is the refractive index of second medium, v1 is the speed of light in firs medium and v2 is the speed of light in second medium.

Example: Find the velocity of the ray in a medium having refractive index 2.

law of refraction example

 

 

 

 

 

Example: A ray coming from medium X is refracted as shown in the figure below while passing to the medium Y. Find ratio of the refractive indexes of the mediums. (sin37º=0, 6 and sin53º=0, 8)

 

 

law of refraction example

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thumb up pls

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1. The first law of refraction states that- the incident ray, the refracted ray and the normal lie on the same plane.
2. The second law of refraction also called the Snell’s Law states that- there is a constant relation between the angle of incident ray (i) and angle of refracted ray (r). This constant is the refractive index of second medium relative to the first medium.
Where n1 is the refractive index of first medium and n 2 is the refractive index of second medium, v1 is the speed of light in first medium and v2 is the speed of light in second medium.
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The following are the laws of refraction:

1)     The incident ray , the refracted ray and the normal to the intergace of two media at the point of incidence , all lie in                the same plane.

2.)     The ratio of sine of angle of incidence to the sine of angle of refraction is constant , for the light of a given colour                    and for the given pair of media. This law is also known as Snell's law of refraction

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1...d incident ray ,d normal 2 d point f incidence nd d refracted ray ol lie on d same plain..

2...d ratio f sin f <i 2 d sin f <r is a constent..4 a given pair f medium nd 4 a given colour....

ie., sin<i /sin<r = a constent..

dis constent is also called as d refractive index f 2nd medium wid rescpect to d 1sd medium.. 

HOPE ITT HELPS U..

ALL D BEST 4 UR XAM..

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 dis s also called as snells law..

4got 2 type first...

srry..

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can anyone explain first law of refraction
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1. the incident ray, the normal and the refracted ray at the point of incidence lie in the same plane.
2. the ratio of sine of angle of incidence and sine of angle of refraction is constant.
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1. the incident ray, the normal and the refracted ray at the point of incidence lie in the same plane. 2. the ratio of sine of angle of incidence and sine of angle of refraction is constant.✌✌✌✌✌✌✌✌✌✌✌✌✌✌
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1] The angle of incidence is equal to angle of refraction which lie on the same plane .
2]  THE ratio of SINE OF ANGLE OF INCIDENCE is equal to SINE OF ANGLE OF REFRACTION.

IT IS THERE IN TEXTBOOK

 
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