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The changing of the path of a light wave while passing from one medium to another medium is called refraction. Refraction is a common phenomenon that occurs in light waves, sound waves and in water waves.

The amount of refraction is determined by the change in the speed of the light wave and the direction of the refracted wave with respect to the initial direction of the wave.

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Refraction of light is a common phenomenon that occurs in our day to day life. An object submerged in water appears closer than it really is when viewed from above. This concept is behind the working of optical lenses. It is used in instruments like glasses, binoculars, cameras, microscopes, and the human eye. Some natural phenomena, like rainbows and mirages, are also due to refraction.

Refraction is based on Snell's law. It states that for a given pair of media the ratio of the sine of the angle of incidence (θ1) to that of the sine of the angle of refraction (θ2) is equal to the ratio and is of the first media with respect to the second media. Further, it is equal to the refractive index of the first medium with respect to the second medium (n2 /n1).

The Refractive index determines the amount of bending of light. It also establishes relations among angle of incidence, angle of refraction, and the refractive index. Mathematically, for a given pair of medium refractive index is given by:

sin θ1/sin θ2 = n2/n1

The angle between the incident & the normal ray is called the angle of incidence 'i', and the angle between the refracted ray & normal is called the angle of refraction 'r'. The laws of refraction of light are:

The normal, the incident & the reflected ray; the entire rays lie in the same plane.

The ratio of the sine of angle of incidence & sine of angle of refraction is a constant and is called a refractive index.

The law of refraction, also called Snell's law, determines the behavior of light-rays when it passes from one medium to another medium.

Consider a ray of light incident on a plane interface between two transparent dielectric media, as shown in the figure below. According to the law of refraction, the normal, the incident ray, and the refracted ray all lie in same plane. Also,

\[n_{1} sin \theta_{1} = n_{2} sin \theta_{2}\]

Where,

θ1 = angle of incidence,

θ2 = angle of refraction.

n1 = refractive index of 1st medium.

n2 = refractive index of 2nd medium.

Thus, according to the law of refraction, light deviates towards the normal in an optical medium with the higher refractive index.

Note that n2>n1 in the figure.

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The refractive index of a dielectric medium having dielectric constant K is represented by the formula:

\[n = \sqrt{k}\]

The table shows the refractive indices of some materials by using yellow light of wavelength λ = 589 nm.

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The incident ray, the refracted ray & the normal all lie in one plane for a given pair of media. Also, the ratio of sine of angle of incidence to that of sine of angle of refraction is a constant.

sin i /sin r = μ

Where,

μ = refractive index of the 2nd medium with respect to the 1st medium.

Place a rectangular glass slab on a white sheet of fixed paper on a drawing board.

Trace the boundary of the glass slab as ABCD.

Now remove the glass slab and draw a line of normal N1N2 at O.

Draw a straight line IO inclined at an angle (let say 300) with the normal. IO is the incident ray.

Fix two pins, pin P, and pin Q on the incident ray IO.

Place the glass slab within the boundary ABCD.

Fix two other pins R and S so that, when seen from the other side of slab P, Q, R, and S appear to lie in a straight line.

Remove the glass slab and the pins after marking the pinpoints P, Q, R, and S.

Join point R and S and produce the line on both sides. The ray O'E is the emergent ray.

Join OO', which is the refracted ray.

You can notice that the incident ray, the refracted ray and the normal are in the same plane. This proves the 1st law of refraction.

Let's Prove the Second Law of Refraction

Draw a circle of radius 'R' with O as the center, such that it cuts the incident and refracted rays at F and G, respectively

Draw perpendiculars from F and G to N1N2

FHO and GKO are right-angled triangles.

sin i = FH/OF

sin r = GK/OG

μ = sin i / sin r

μ = FH/OG * OG/GK

μ = FH/GK

Measure the lengths of FH and GK and write them in a table.

Do the same for different angles of incidence.

Find the ratio FH/GK for different values of incidence 'i'.

It is found that FH/GK has set value for each observation.

This proves the laws of refraction.

FAQ (Frequently Asked Questions)

1. What are sin i and sin r?

Ans: The sine of the angle of incidence is 'sin i,' and the sine if the angle of refraction is 'sin r.' They are related by the relation of sin i/sin r = n.

2. A biconvex lens of focal length 'f ' forms a circular form of the sun of a radius 'r' in a focal plane. Then, which of the following options is true?

πr² ∝ f

πr² ∝ f²

If 'f 'is doubled, the intensity will increase.

If a black sheet covers the lower part, the image's area is equal to πr²/2

Ans: b

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From the above representation, r = f tan α

Hence, πr² ∝ f².

3. What is an Angle of Refraction?

Ans: The angle of refraction is an angle between a refracted ray and the normal drawn at the point of incidence.

4. Why is Sin Used in Snell's Law?

Ans: Sin is used in Snell's law because the sine of the incidence and refraction angles are needed to determine the refractive index.