Aarti Gupta
Last Activity: 10 Years ago
Dear student i am explaining you how the angle of deviation can be found.You will surely understand how to find the angle of deviation.Allk the best.
Le us suppose a ray KL is incident on the face AB of the prism at the point F( for the figure see below) where N1LO is the normal and∠i1is the angle of incidence.Since the refraction takes place from air to glass, therefore,the refracted ray LM bends toward the normal such that∠r1is the angle of refraction.Ifµ be the refractive index of glass with respect to air, then
µ = sin i/sin r ------- (By Snell’s law)
The refracted ray LM is incident on the face AC at the point M where N2MO is the normal and∠r2is the angle of incidence.Since the refraction now takes place from denser to rarer medium, therefore,the emergent ray MN such that∠i2is the angle of emergence.Now in the absence of the prism,the incident ray KL would have proceeded straight, but due to refraction through the prism,it changes its path along the direction PMN. Thus,∠QPN gives the angle of deviation ‘δ’, i.e. the angle through which the incident ray gets deviated in passing through the prism.
Thus, δ = i1– r1+ i2-r2 ….... (1)
δ = i1+ i2– (r1+r2)
Again, in quadrilateral ALOM,
∠ALO +∠AMO = 2rt∠s [Since,∠ALO = ∠AMO = 90º]
So,∠LAM +∠LOM =2rt∠s [Since, Sum of four ∠s of a quadrilateral = 4 rt∠s] ….... (2)
Also in?LOM,
∠r1+∠r2+∠LOM = 2rt∠s …... (3)
Comparing (2) and (3), we get
∠LAM =∠r1+∠r2
A =∠r1+∠r2
Using this value of∠A, equation (1) becomes,
δ = i1+ i2- A
ori1+ i2=A +δ …... (4)
This is how the angle of deviation can be found
