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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.
Describe an activity to show that the colours of white light splitted by a glass prism can be recombined to get white light by another identical glass prism. Also, draw a ray diagram to show the recombination of the spectrum of white light.
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 certain material has refractive indices 1.56, 1.60 and 1.68 rfor red, yellow and violet lightespectively. (a) Calculate the dispersive power. (b) Find the angular dispersion produced by a thin prism of angle 6° made of this material.
The minimum deviations suffered by, yellow and violet beams passing through an equilateral transparent prism are 38.4°, 38.7° and 39.2° respectively. Calculate the dispersive power of the medium.
A thin prism of crown glass (μr = 1.515, μv = 1.525) and a thin prism of flint glass (μr = 1.612, μv = 1.632) are placed in contact with each other. Their refracting angles are 5.0° each and are similarly directed. Calculate 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.
Calculate dispersive power of a transparent material given : nv = 1.56, nr = 1.54, ny = 1.55.
How does the angle of minimum deviation of a glass prism vary if the incident violet light is replaced by red light?
