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प्रश्न
Using Huygen’s wave theory of light, prove Snell’s law of refraction of light.
उत्तर
Consider a plane wavefront AB incident on a surface PQ separating two medium 1 and 2. The medium 1 is a rarer medium of refractive index n1 in which light travels with a velocity c1. The medium 2 is a denser medium of refractive index n2 in which light travels with a velocity c2.
The angle between the incident ray FA and the normal NA at the point of incidence A is equal to i.
The angle is also equal to the angle between the incident plane wavefront AB.
Similarly, the angle between the refracted wavefront and the surface of separation PQ is equal to the angle of refraction r.
i.e., ∠ADC = r
Consider the triangles ΔBAD, ΔACD figure below.
sin i = sin ∠BAD = `"BD"/"AD" = ("c"_1"t")/"AD"`
sin r = sin ∠ADC = `"AC"/"AD" = ("c"_2"t")/"AD"`
`(sin "i")/(sin "r") = ("c"_1 "t")/("c"_2 "t") = "c"_1/"c"_2` = constant
This constant is called the refractive index of the second medium (2) with respect to the first medium (1).
`"c"_1/"c"_2 = "n"_2/"n"_1` = 1n2
This equation proves the Snell's law.
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संबंधित प्रश्न
Use Huygens’ geometrical construction to show the propagation of plane wavefront a rarer medium (1) to a denser medium (2) undergoing refraction.
Hence derive Snell’s law of refraction.
Derive Snell’s law of refraction using Huygens’s wave theory.
Define the term, “refractive index” of a medium. Verify Snell’s law of refraction when a plane wavefront is propagating from a denser to a rarer medium. Solution
Answer the following question.
Define the term, "refractive index" of a medium. Verify Snell's law of refraction when a plane wavefront is propagating from a denser to a rarer medium.
A small bulb is placed at the bottom of a tank containing water to a depth of 80 cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of water is 1.33. (Consider the bulb to be a point source.)
According to Snell’s law, ______.
For small angles Snell’s law becomes ______.
Draw the shape of refracted wavefront when the plane incident wave undergoes refraction from optically denser medium to rarer medium. Hence prove Snell’s law of refraction.
If light passes near a massive object, the gravitational interaction causes a bending of the ray. This can be thought of as happening due to a change in the effective refractive index of the medium given by n(r) = 1 + 2 GM/rc2 where r is the distance of the point of consideration from the centre of the mass of the massive body, G is the universal gravitational constant, M the mass of the body and c the speed of light in vacuum. Considering a spherical object find the deviation of the ray from the original path as it grazes the object.
A ray of light is incident on a glass prism of refractive index µ and refracting angle A. If it just suffers total internal reflection at the other face, obtain a relation between the angle of incidence, angle of prism and critical angle.
