Refractive Index of material of a Prism (i-D curve method)

Refractive Index of material of a Prism (i-D curve method)

AIM: To determine refractive index of the material of the given prism by the method of i-d curve.
APPARATUS:i)Drawing board ii)Prism iii)Drawing pins iv)Needle point steel pins  v) Drawing sheet vi)Scale,set square,protractor  and a sharp pencil.
PRINCIPLE:When the prism is at minimum deviation position “Angle of incidence \angle{i} = Angle of emergence \angle{e} i.e (\angle{i}= \angle{e}) and the angle of refractions at both the surfaces of the prism will be equal i.e \angle{r_1}= \angle{r_2}. From geometry we have
d=i+e-A    ;  {r_1}+{r_2}= A
but when the prism is in minimum deviation d=D_m ,
D_m=2i-A since  \angle{i}= \angle{e}
\implies2i = A+D_m
\implies i = \frac{A+D_m}{2} – – – – – – –  –  – – – – (a)
and 2r =A since \angle{r_1}= \angle{r_2}= \angle{r}
\impliesr = \frac{A}{2} – – – – – – –  –  – – – – (b)
But according to snell’s law \mu= \frac{Sini}{Sinr}
substituting the values of  i and r in the above equation from equations (a) and (b) we get
\mu= \frac{sin\frac{(A+D_m)}{2}}{sin \frac{A}{2}}
THEORY:If the angle of the prism is \angle{A} then angle of deviation \angle{D} = \angle{i}+\angle{e}-\angle{A} and \angle{r_1}+\angle{r_2}= \angle{A}
If \angle{A} is the angle of the prism,\angle{D_m} the angle of minimum deviation.
Then the refractive index of the material of the prism  \mu= \frac{sin\frac{(A+D_m)}{2}}{sin \frac{A}{2}}
PROCEDURE: We can divide the entire procedure of this experiment in to two parts i) we have to first determine the angle  of the prism A then ii) We have to  determine the angle of minimum deviation D of the prism.
Part i: Determine the angle of the prism A:Place the drawing board on the table and fix the drawing sheet on the drawing board using drawing pins.Place the prism on the drawing sheet,holding the prism trace the outer boundary of the prism which will be triangle.Mark the three vertices of the triangle as A,B and C.Now draw two parallel lines so that the edge A lies symmetrically between parallel lines.
to find angle of prism
Then two pins are fixed on one of the lines at points P and Q.Looking through the face AB two more pins are fixed at the points R and S so that the reflective images of the pins at P an Q lie in the same straight line with these two pins without any parallax error.Now join the points R and S using a scale .The RS line represents the reflected ray of PQ.In the same way repeat the procedure on the other face of the prism AC, to get the reflected images G,H of the incident ray passing through EF.Remove the prism and extend the st.lines passing through RS and GH in to triangle ABC so that they meet at a point O.
Measure the angle ROG which will be equal to 2A
Hence \angle{A} = \frac{\angle{ROG}}{2}
Part ii:Determine the angle of minimum deviation \angle{D_m}:Fix the drawing sheet on the drawing board using drawing pins,keep the prism on the paper and trace the prism.The trace will give us a triangle ABC.
to find angle of prism
AB reflecting surface , AC  refracting surface and BC is the base of the prism.Draw a normal line MN to the reflecting surface at N.Draw a incident line PQ making some angle (>30degrees) with the normal line MN.Now place the prism on its trace along ABC.Fix two pins on the incident ray at two points P and Q .Now observing through the face AC two pins S and U are fixed so that these two pins at S and U will be in the line with P and Q.Remove the prism join the points S and U with a st line which meets the face AC at R.Extend the incident ray PQ forward and emergent ray SU backwards till the meet at O.
Measure the \angle{TOR}=d.
repeat the experiment in the above said procedure for various angles of incidences i.e 35,40,45,50,55 ……. and measure the respective angles of deviations d1,d2,d3,d4,d5….. record these values in the table. Angle of incidence ( i) Angle of deviation ( d )

i-d curve:Now draw a graph taking the angles of incidences(i) on X-axis and the angles of deviations(d) on the Y-axis.join these points with a smooth curve which will be a parabola.
angle of minimum deviation by i-d curve method
From the graph the angle of minimum deviation can be calculated.
OBSERVATIONS: i) Angle of the prism A =
ii) Angle of minimum deviation D_m =            ( from graph)
substituting the values of the angle of prism A and the angle of minimum deviation D_m in the formula of refractive index \mu= \frac{sin\frac{(A+D_m)}{2}}{sin \frac{A}{2}}, we can calculate the refractive index of the material of the prism.
PRECAUTIONS: i)Pins should be fixed perfectly vertical ii)while fixing the pins in line with the refractive or reflective images of incident rays care should be taken for the parallax error.iii) there should be some space between the pins iv)pins should not be disturbed during the experiment v)Same edge of the prism should be taken as vertex A for all the observations vi) Clean both the faces AB and AC of the prism proper before taking the readings.
RESULT: Refractive index of the material of the prism  \mu=