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प्रश्न
Plot a graph to show the variation of the angle of deviation as a function of the angle of incidence for light passing through a prism. Derive an expression for the refractive index of the prism in terms of angle of minimum deviation and angle of the prism.
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उत्तर
If the angle of incidence is increased gradually, then the angle of deviation first decreases, attains a minimum value (δm) and then again starts increasing.
When the angle of deviation is minimum, the prism is said to be placed in the minimum deviation position.
There is only one angle of incidence for which the angle of deviation is minimum.
When δ = δm [prism in minimum deviation position],
e = i and r2 = r1 = r …..(i)
∵ r1+r2=A
From (i), we get
r + r = A
`r=A/2`
Also, we have
A + δ = i + e
Substituting δ = δm and e = i,
A + δm = i + i
`i=(A+delta_m)/2`
∵`mu=sin i/sin r`
`:.mu=(sin(A+delta_m/2)/Sin (A/2))`
संबंधित प्रश्न
Two monochromatic rays of light are incident normally on the face AB of an isosceles right-angled prism ABC. The refractive indices of the glass prism for the two rays '1' and '2' are respectively 1.38 and 1.52. Trace the path of these rays after entering through the prism.
A ray of light incident normally on one face of a right isosceles prism is totally reflected, as shown in fig. What must be the minimum value of refractive index of glass? Give relevant calculations.
If three identical prisms are combined, is it possible to pass a beam that emerges undeviated? Undispersed?
A prism can produce a minimum deviation δ in a light beam. If three such prisms are combined, the minimum deviation that can be produced in this beam is _______________.
By properly combining two prisms made of different materials, it is possible to
(a) have dispersion without average deviation
(b) have deviation without dispersion
(c) have both dispersion and average deviation
(d) have neither dispersion nor average deviation
A thin prism is made of a material having refractive indices 1.61 and 1.65 for red and violet light. The dispersive power of the material is 0.07. It is found that a beam of yellow light passing through the prism suffers a minimum deviation of 4.0° in favourable conditions. Calculate the angle of the prism.
The refractive index of a material M1 changes by 0.014 and that of another material M2 changes by 0.024 as the colour of the light is changed from red to violet. Two thin prisms, one made of M1(A = 5.3°) and the other made of M2(A = 3.7°) are combined with their refracting angles oppositely directed. (a) Find the angular dispersion produced by the combination. (b) The prisms are now combined with their refracting angles similarly directed. Find the angular dispersion produced by the combination.
A ray of light is incident on a prism whose refractive index is 1.52 at an angle of 40°. If the angle of emergence is 60°, calculate the angle of the prism.
An equilateral glass prism has a refractive index 1.6 in the air. Calculate the angle of minimum deviation of the prism, when kept in a medium of refractive index `4sqrt(2)"/"5.`
Prove that in case of a prism, i + e = A + δ, where the symbols have their usual meanings.
