Advertisements
Advertisements
Question
A narrow beam of monochromatic light, PQ, is incident normally on one face of an equiangular glass prism of refractive index 1.45. When the prism is immersed in a certain liquid, the ray makes a grazing emergence along the other face (See figure). Find the refractive index of this liquid. 
Solution
When the prism is immersed in the liquid and the incident ray emerges along AC, it is clear that it must be incident at the critical angle C on the face AC.
∠A + ∠ARQ = ∠C + ∠ARQ
From the figure, ∴ ∠C = ∠A = 60°
The critical angle when the prism is immersed in the liquid is 60°.
If μg is the refractive index of the material of the prism w.r.t. liquid
Then `""^l µ_g = 1/sin"C" = 1/sin60° = 1/(sqrt3/2) = 2/sqrt3`
`""^l µ_g = 2/sqrt3`
Also, we know that `""^l µ_g =( ""^aµ_g)/( ""^aµ_l)`
`""^aµ_l =( ""^aµ_g)/( ""^l µ_g )`
= `1.45/2 xx sqrt3`
= 1.45 x 0.866
= 1.256
APPEARS IN
RELATED QUESTIONS
A ray PQ incident normally on the refracting face BA is refracted in the prism BAC made of material of refractive index 1.5. Complete the path of ray through the prism. From which face will the ray emerge? Justify your answer.
A ray PQ incident on the refracting face BA is refracted in the prism BAC as shown in the figure and emerges from the other refracting face AC as RS such that AQ = AR. If the angle of prism A = 60° and refractive index of material of prism is `sqrt3 `. Calculate angle θ.
State any two difference between the primary rainbow and secondary rainbow
Figure shows a ray of light passing through a prism. If the refracted ray QR is parallel to the base BC, show that (i) r1 = r2 = A/2 and (ii) angle of minimum deviation, Dm = 2i − A.
Out of blue and red light which is deviated more by a prism? Give reason.
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.
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).
Define angular dispersion.
The refractive indices of material for red, violet and yellow colour light are 1.52, 1.62 and 1.59 respectively.
Calculate the dispersive power of the material. If the mean deviation is 40°. What will be the angular dispersion produced by a prism of this material?
