why is the graph ofprism experiment u shaped
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Let
i1 and i2 be the angle of incidence and emergence of prism of angle A. r1 and r2 be the angle of refraction at first surafce and incidence angle at second surface at prism (common notation in most of books)
Then deviation at first surface is given by
d1 = i1 - r1
Deviation at second surface is given by
d2 = i2 - r2
Then total deviation by prism is given by
δ=d1+d2=i1+i2−(r1+r2)=i1+i2−A
From the reversibility of rays it can seen that i1and i2 can be interchanged, when they interchanged r1 and r2 interchanged but the total deviation remains unchanged, thus for same deviation there are two possible value of incidence i1 and i2 and when i1 and i2 are equal we get minimum deviation, hence we get the angle of incidence and deviation curve like flattered U.
When i1 is angle of incidence i2 will be angle of emergence and vice versa, deviation remains same.When i1 increases i2 decreases, deviation start decreasing as light from rarer medium entering the denser medium at first surface and hence bend towards the normal and at the second surface away from the normal i.e. at first refraction refracted angle becomes more than the emergent ray at the second surface i.e. r1 is more than r2.After attaining a minimum deviation (for which r1 = r2) angle of incidence and emergence interchanged, the initial direction of the incident light in the first refraction becomes smaller than the initial direction of the incident light in the second refraction ie r2 is more than r1, so that the deviation increases.
This happens because of dependence of the angle of deviation of prism on the angle of incidence, angle of emergence emergence, angle of prism, refractive index of material, wavelength of light used and more importantly on the symmetry of the ray with respect to the two faces of the prism
i1 and i2 be the angle of incidence and emergence of prism of angle A. r1 and r2 be the angle of refraction at first surafce and incidence angle at second surface at prism (common notation in most of books)
Then deviation at first surface is given by
d1 = i1 - r1
Deviation at second surface is given by
d2 = i2 - r2
Then total deviation by prism is given by
δ=d1+d2=i1+i2−(r1+r2)=i1+i2−A
From the reversibility of rays it can seen that i1and i2 can be interchanged, when they interchanged r1 and r2 interchanged but the total deviation remains unchanged, thus for same deviation there are two possible value of incidence i1 and i2 and when i1 and i2 are equal we get minimum deviation, hence we get the angle of incidence and deviation curve like flattered U.
When i1 is angle of incidence i2 will be angle of emergence and vice versa, deviation remains same.When i1 increases i2 decreases, deviation start decreasing as light from rarer medium entering the denser medium at first surface and hence bend towards the normal and at the second surface away from the normal i.e. at first refraction refracted angle becomes more than the emergent ray at the second surface i.e. r1 is more than r2.After attaining a minimum deviation (for which r1 = r2) angle of incidence and emergence interchanged, the initial direction of the incident light in the first refraction becomes smaller than the initial direction of the incident light in the second refraction ie r2 is more than r1, so that the deviation increases.
This happens because of dependence of the angle of deviation of prism on the angle of incidence, angle of emergence emergence, angle of prism, refractive index of material, wavelength of light used and more importantly on the symmetry of the ray with respect to the two faces of the prism
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