Advertisements
Advertisements
Question
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.
Solution
If μ'v and μ'r are the refractive indices of material M1, then we have:-
μ'v – μ'r = 0.014
If μv and μr are the refractive indices of material M2, then we have:-
μv – μr = 0.024
Now,
Angle of prism for M1, A' = 5.3°
Angle of prism for M2, A = 3.7°
(a) When the prisms are oppositely directed, angular dispersion (δ1) is given by
δ1 = (μv – μr)A – (μ'v – μ'r)A'
On substituting the values, we get:-
δ1 = 0.024 × 3.7° – 0.014 × 5.3°
= 0.0146°
So, the angular dispersion is 0.0146°.
(b) When the prisms are similarly directed, angular dispersion (δ2) is given by
δ2 = (μv – μr)A + (μ'v – μ'r)A'
On substituting the values, we get:-
δ2 = 0.024 × 3.7° + 0.014 × 5.3°
= 0.163°
So, the angular dispersion is 0.163°.
APPEARS IN
RELATED QUESTIONS
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.
A ray of light passes through an equilateral glass prism such that the angle of incidence is equal to the angle of emergence and each of these angles is equal to 3/4 of angle of prism. Find the angle of deviation.
For any prism, prove that :
'n' or `mu = sin((A + delta_m)/2)/sin(A/2)`
where the terms have their usual meaning
Draw the ray diagram showing refraction of light through a glass prism and hence obtain the relation between the refractive index μ of the prism, angle of prism and angle of minimum deviation.
Give the formula that can be used to determine refractive index of materials of a prism in minimum deviation condition ?
The equation \[\omega = \frac{\mu_u - \mu_r}{\mu - 1}\] was derived for a prism having small refracting angle. Is it also valid for a prism of large refracting angle? Is it also valid for a glass slab or a glass sphere?
The angular dispersion produced by a prism ___________ .
If a glass prism is dipped in water, its dispersive power ___________ .
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.
Three thin prisms are combined as shown in figure. The refractive indices of the crown glass for red, yellow and violet rays are μr, μy and μv respectively and those for the flint glass are μ'r, μ'y and μ'v respectively. Find the ratio A'/A for which (a) there is no net angular dispersion, and (b) there is no net deviation in the yellow ray.
A thin prism of angle 6.0°, ω = 0.07 and μy = 1.50 is combined with another thin prism having ω = 0.08 and μy = 1.60. The combination produces no deviation in the mean ray. (a) Find the angle of the second prism. (b) Find the net angular dispersion produced by the combination when a beam of white light passes through it. (c) If the prisms are similarly directed, what will be the deviation in the mean ray? (d) Find the angular dispersion in the situation described in (c).
The deviation produced for violet, yellow and red lights for crown glass are 3.75°, 3.25° and 2.86° respectively. Calculate the dispersive power of the crown glass.
In a regular prism, what is the relation between angle of incidence and angle of emergence when it is in the minimum deviation position?
Calculate dispersive power of a transparent material given : nv = 1.56, nr = 1.54, ny = 1.55.
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.`
How does the angle of minimum deviation of a glass prism vary if the incident violet light is replaced by red light?
Define angular dispersion.
