PHYSICS Project
PRISM Calculation of Minimum angle of deviation And Refractive Index
Certificate This is to certify that the project titled “PRISM, Calculation of Minimum Angle of Deviation and Refractive Index” has been successfully submitted by _______ of class 12 for the fulfillment of the curriculum of the Central Board of Secondary Education (CBSE) for the academic session 2015-2016.
Signature of Teacher Principal
INDEX S.N o. 1. 2. 3. 4. 5.
Content Aim of Experiment Theory Observations Calculations Precautions
Pag e 1 2-3 4 4 5
Aim of experiment To measure the refractive index of a prism and the minimum angle of deviation by using a light ray.
THEORY Figure shows the passage of light through a triangular prism ABC. The angles of incidence and refraction at the first face AB are i and r 1, while the angle of incidence (from glass to air) at the second face AC is r 2 and the angle of refraction or emergence e. The angle between the emergent ray RS and the direction of the incident ray PQ is called the angle of deviation, δ. In the quadrilateral AQNR, two of the angles at the vertices Q and R) are right angles. Therefore, the sum of the their angles of the quadrilateral is 180º. ∠ A +∠QNR=180º
(i)
From the triangle QNR, r 1+ r 2+∠ QNR=180 º
(ii)
Comparing these two equations, we get r 1+ r 2=A
(iii)
The total deviation δ is the sum of deviations at the two faces, δ = (i – r1) + (e – r2) that is, δ =i+e – A
(iv)
Thus, the angle of deviation depends on the angle of incidence. A plot between the angle of deviation and angle of incidence is shown in the graph. You can see that, in general, any given value of δ, except for i = e, corresponds to two values i and hence of e. This, in fact, is expected from the symmetry of i and e in Eq. (9.35), i.e., δ remains the same if I and e are interchanged. Physically, this is related to the fact that the path of ray in diagram can be traced back, resulting in the same angle of deviation. At the minimum deviation Dm, the refracted ray inside the prism becomes parallel to its base. We have
δ=δ m , i=e
This implies:
r 1=r 2
Equation (iii) gives:
2 r= A∨r=
A 2
(v)
In the same way, Eq. (iv) gives δ m=2 i – A ,∨i=
A+ δ m 2
(vi)
The refractive index of the prism (by Snell’s Law) is:
n21 =
n2 = n1
A+ δm ) 2 A sin 2
sin (
( )
(vii)
The angles A and δm can be measured experimentally. Equation (vii) thus provides a method of determining refractive index of the material of the prism. In my working model of this experiment, I have made use of a laser light to observe the deviation that is caused by the prism. The deviation is thereafter measured by measuring the angle of incidence and angle of emergence by the equation (iv), i.e. δ =i+e – A
The observations have been noted in the observation table accordingly. Thereafter, I have calculated the refractive index of the prism
OBSERVATIONS Angle of prism = 60 ° . S.
Angle of Incidence
No.
(i0)
1. 2. 3. 4. 5.
600 550 450 400 350
Angle of Emergence( e 430 420 450 530 650
Angle of Deviation( )
0
δ
0
)
430 370 300 330 400
CALCULATIONS From the readings above, a plot of δ
0
vs. i0 can be made. It is visible from
the graph and the readings as well, that the minimum angle of deviation is = 30 ° .
Also, refractive index of the prism can be calculated by the equation:-
n21 =
n2 = n1
A+ δm ) 2 A sin 2
sin (
( )
Hence refractive index of the prism (n21) is =
sin ( 45 ) sin ( 30 )
= √ 2 = 1.414
Precautions Angle of incidence should lie b/w 35-60 degree. Same angle of prism should be used for all observation.
SOURCES OF ERROR The angle of incidence and angle of emergence might not be observed accurately.
BIBLIOGRAPHY The following resources have been cited to complete the project:
www.ncert.nic.in/ncerts/textbook/textbook.htm - The NCERT Textbooks online service. https://en.wikipedia.org/wiki/Prism - The Wikipedia article on Prisms. www.google.com – Search engine for other content. Textbooks for reference: NCERT Physics – Class 12 Halliday/ Resnick/Walker Physics by Manish K. Singhal