Hellooooo everyone...... Look at the above figure. It shows the refraction of a light ray through this glass prism..... As we know, a prism (of denser medium) always bends light towards its base, here it happens the same. Look at angle of incidence, angle of prism (r1 + r2) and angle of deviation carefully.
Two questions are there from here.
1] If the value of angle of incidence (i1) on the first surface of the prism increases, what will happen to the angle of emergence (i2), on the other surface of that prism? (i.e., will the angle of emergence increase or decrease?). Prove your answer mathematically.
[Hint : Snell's law can be used and logics like <A = r1 + r2, can be used. Using these two informations you have to prove]
2] Logically, (and not mathematically) show that, during minimum deviation, i1 becomes equal to i2.
[Hint : You can use the logic of principle of reversibility of light for proving this.]
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Answers
ANSWER:-
The angle of incidence is equal to the angle of emergence. This is always true, provided you are using a glass block with parallel sides. The incident ray will also be parallel to the emergent ray. This is the angle of refraction. This has to do with a ray of light entering a block of glass, which refracts, or bends, it so that it emerges on the other side parallel to the incident ray, but displaced.
The equation relating the angles of incidence (Θi) and the angle of refraction (Θr) for light passing from air into water is given as
Observe that the constant of proportionality in this equation is 1.33 - the index of refraction value of water. Perhaps it's just a coincidence. But if the semi-cylindrical dish full of water was replaced by a semi-cylindrical disk of Plexiglas, the constant of proportionality would be 1.51 - the index of refraction value of Plexiglas. This is not just a coincidence. The same pattern would result for light traveling from air into any material. Experimentally, it is found that for a ray of light traveling from air into some material, the following equation can be written.
where nmaterial = index of refraction of the material
This study of the refraction of light as it crosses from one material into a second material yields a general relationship between the sines of the angle of incidence and the angle of refraction. This general relationship is expressed by the following equation:
where Θi ("theta i") = angle of incidence
Θr ("theta r") = angle of refraction
ni = index of refraction of the incident medium
nr = index of refraction of the refractive medium
This relationship between the angles of incidence and refraction and the indices of refraction of the two media is known as Snell's Law. Snell's law applies to the refraction of light in any situation, regardless of what the two media are.
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The angle of incidence is equal to the angle of emergence. This is always true, provided you are using a glass block with parallel sides. The incident ray will also be parallel to the emergent ray. This is the angle of refraction. This has to do with a ray of light entering a block of glass, which refracts, or bends, it so that it emerges on the other side parallel to the incident ray, but displaced.
The equation relating the angles of incidence (Θi) and the angle of refraction (Θr) for light passing from air into water is given as
Observe that the constant of proportionality in this equation is 1.33 - the index of refraction value of water. Perhaps it's just a coincidence. But if the semi-cylindrical dish full of water was replaced by a semi-cylindrical disk of Plexiglas, the constant of proportionality would be 1.51 - the index of refraction value of Plexiglas. This is not just a coincidence. The same pattern would result for light traveling from air into any material. Experimentally, it is found that for a ray of light traveling from air into some material, the following equation can be written.
where Θi ("theta i") = angle of incidence
Θr ("theta r") = angle of refraction
ni = index of refraction of the incident medium
nr = index of refraction of the refractive medium