How do you find experimentally the refractive index of material of prism
Answers
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 of emergence i.e () and the angle of refractions at both the surfaces of the prism will be equal i.e . From geometry we have
d=i+e-A ;
but when the prism is in minimum deviation d= ,
=2i-A since
2i = A+
i = – – – – – – – – – – – – (a)
and 2r =A since
– – – – – – – – – – – – (b)
But according to snell’s law
substituting the values of i and r in the above equation from equations (a) and (b) we get
THEORY:If the angle of the prism is then angle of deviation and
If is the angle of the prism, the angle of minimum deviation.
Then the refractive index of the material of the prism
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.
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
Part ii:Determine the angle of minimum deviation :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.
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 .
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.
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.
From the graph the angle of minimum deviation can be calculated.
OBSERVATIONS: i) Angle of the prism A =
ii) Angle of minimum deviation = ( from graph)
substituting the values of the angle of prism A and the angle of minimum deviation in the formula of refractive index , 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
Explanation:
Aim : Finding the refractive index of the prism.
Material required : Prism, piece of white chart of size 20 x 20 cm, pencil, pins, scale and protractor.
Procedure :
Take a prism and place it on the white chart in such a way that the triangular base of the prism is on the chart.
Draw a line around the prism using a pencil. Remove the prism.
It is a triangle. Name its vertices P, Q and R.
Find the angle between PQ and PR. This is the angle of the prism (A).
Mark M on the side of triangle PQ and also draw a perpendicular to the PQ at M.
Place the centre of the protractor at M and along the normal mark an angle of 30° and then draw line up to M.
This angle is angle of incidence and note it in a table.
Place the prism in its position again.
Now fix two pins vertically on the line at point A and B.
Look for the images of pins through the prism from the other side and fix another two pins at points C and D in such a way that all the four pins appear to lie along same straight line.
Now remove the prism and take out pins.
Draw a line joining the two pin-holes formed by the pins to meet surface PR.
The angle between the normal at N and the emergent ray is the angle of emergence.
Join M and N. A,B,M,N, C, D represent the path of light.
Extend both incident, emergent rays tell they meet at a point ‘O’.
The angle between these two rays is angle of deviation denoted by ‘D’.
Do the same for various angles of incidence such as 40°, 50° etc.
If we take angle of incidence along x-axis and the angle of deviation along y-axis we get the graph as shown in figure.
The refractive index of prism n = Sin [(A + D)/2] / sin A/2