Draw a ray diagram to show refraction of a ray of monochromatic light passing through a glass prism.Deduce the expression for the refractive index of glass in terms of angle of prism and angle of minimum deviation.
i- angle of incidence
r and r'-angles of refractions
- angle of deviation
Consider light passing through a prism ABC as shown
As shown, the angles of incidence and refraction at the first face AB are i and r, while the angle of incidence (from glass to air) at the second face AC is r' and the angle of emergence i'. The angle between the emergent ray RS and incident ray direction PQ is called the angle of deviation, .
In the quadrilateral AQNR, two of the angles (at the vertices Q and R) are right angles. Therefore, the sum of the other angles of the quadrilateral is 1800
A +QNR = 1800
From triangle QNR,
r + r '+QNR = 1800
Comparing, we get
r +r' = A-------------------(1)
The total deviation is the sum of deviations at the two faces:
A plot between angle of deviation and the angle of incidence is seen to be as follows
It is seen that in general, any given value ofcorresponds to two values i and i'. Physically, this is due to the fact that the path of the ray can be traced back, resulting in the same angle of deviation.
At the minimum deviation, = Dm ,
i = i' which implies that r = r'.
Then, we get from (1)
2r = A
r = A/2
Similarly, from equation (2)
Dm = 2i - A
i = (A +Dm) / 2
The refractive index of the prism with respect to the medium outside is
This relation is called the prism formula.It is used for accurate determination of refractive index of a transparent medium.
Angles A and Dm can be measured experimentally with good precision.
So, equation provides a good way of measuring refractive index of a prism.
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