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PSR HSR TOTAL CURRENT in MA 0.5 0.01 0.5+(1.5*0.01)=0.51 0 0.5 0.01 0.5+(2.5*0.01)=0.52 0 0.5 0.01 0.5+(3*0.01)=0.53 0 0.5 0.01 0.5+(5*0.01)=0.55 0.000106 0.5 0.01 0.5+(6.4*0.01)=0.64 0.01605 0.5 0.01 0.5+(8*0.01)=0.58 0.054131 0.5 0.01 0.5+(9*0.01)=0.59 0.12352 1 0.01 1+(10*0.01)=1.1 0.143 1 0.01 1+(11*0.01)=1.11 0.0296 1 0.01 1+(14*0.01)=1.14 0.004 1 0.01 1+(15*0.01)=1.15 0.000023 1 0.01 1+(1
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Background Coherent sources of light, Concept of Interference, Interference by division
of wave front and amplitude, Interference in thin films, Newton’s ring apparatus.
Aim: To determine the wavelength of sodium light by Newton’s Ring method.
Apparatus: A nearly monochromatic source of light (source of sodium light), a plano-convex lens C, an optically plane glass plate P, an optically flat glass plate G in- clined at an angle of 45◦, a travelling microscope with measuring scale and a spherometer.
Theory:
When a parallel beam of monochromatic light is incident normally on a combination of a plano-convex lens C and a glass plate P, as shown in fig.1(a), a part of each incident ray is reflected from the lower surface of the lens, and a part, after refraction through the film between the lens and the plate, is reflected back from the surface of glass plate. These two reflected rays are coherent, hence they will interfere and produce a system of alternate dark and bright rings (see fig.1(b)) with the point of contact between the lens and the plate at the center. These rings are known as Newton’s rings.
(a) Experimental set-up (b) Newton’s rings Figure 1
In general, the path difference between the reflected light beams which are undergoing interference (for oblique incidence) is given by
∆ = 2μtcosθ − λ 2 , (1)
where additional path difference of λ 2 is because one of the interfering beam is reflected from film to glass surface. Also, θ is the angle of incidence. For normal incidence θ=0◦^ and hence, the path difference will be
∆ = 2μt − λ 2. (2)
by using Eq.(4) and Eq.(5), we have
r n^2 = nλRμ. (6)
Using rn=D 2 n , we can write following relation for diameter of nth, ring
D n^2 = 2r^2 n = nλRμ. (7)
The diameter of some mth dark fringe will be
D^2 m = mλRμ. (8)
Subtracting Eq.(7) and Eq.(8), we can write following relation
λ = D
(^2) n − D (^2) m 4 R(n − m)μ.^ (9)
Above equation is used to find the wavelength of monochromatic light using Newton ring’s method, in which material of refractive index μ is immersed between plano-convex lens and glass plate. If air is enclosed as thin film having μ=1, then Eq.(9) becomes
λ = D n^2 −^ D^2 m 4 R(n − m).^ (10)
The radius of curvature, R is calculated by spherometer (see fig.3) using following relation R = l
2 6 h +^
h
In above, l is the mean length of the three sides of equilateral triangle formed by joining the tips of three outer legs and h represents the height of the central screw above or below the plane of the outer legs. Procedure: The experimental set-up used for the experiment is shown in fig.1(a).
Figure 3: Spherometer.
Sr. no. Spherometer readings on h (cm) l (cm) convex surface plane surface
Table 2: Calculations of h and l.
Wavelength
Sr. no.
λ = 4 DR^2 n(−n−Dm^2 m) μ (nm)
Table 3: Calculations for wavelength λ.
Results:
Precautions: Notice that as you go away from the central dark spot the fringe width decreases. In order to minimize the errors in measurement of the diameter of the rings the following precautions should be taken:
Sample viva voce questions :