Theory: When a parallel beam of monochromatic light is incident normally on a combination of a planoconvex lens L and a glass plate P, as shown in the fig below, a part of each incident ray is reflected from the lower surface of the lens n and a part after refraction through the air film between the lens and the plate, is reflected back from plate surface. These two reflected rays are coherent. Hence the reflected rays will interfere and produce a system of alternate dark and bright rings with the point of contact between the lens and the plate as the center. These rings are known as Newton’s rings.
If D_{m} is the diameter of the mth bright ring, counted from the center, we have
\[\frac{D_{m}}{4R}=(2m+1)\frac{\lambda}{2}………..(i)\]
where R is the radius of curvature of the lower surface of the lens L, and λ is the wavelength of light.
For the (m + n) th bright ring
\[\frac{D_{m+n}}{4R}=(2m+2n+1)\frac{\lambda}{2}………..(ii)\]
Where D_{m+n} is the diameter of the (m+n)th ring.
From (i) and (ii) we get
\[R=\frac{D_{m+n}^{2}D_{m+n}^{2}}{4n\lambda}\]
or
\[\lambda=\frac{D_{m+n}^{2}D_{m+n}^{2}}{4nR}………(iii)\]
Equation (iii) is used as the working formula for calculating R
Experimental Results:
1.Determination of the vernier constant of the horizontal scale of the microscope
2.Table for the measurement of diameter of the rings
Order no.  Reading of microscope (cm)  Diameter D
(L ~ R) (cm) 

Left (L)  Right (R)  
M.S.R  V.S.R  Total  M.S.R  V.S.R  Total  
3.Table for the measurment of the wavelength:
R = 110cm
No of set 
Order no 
D(cm) 
D^{2} 
\[{D_{m+n}^{2}D_{n}^{2}} \] 
λ

Mean λ 
Result:
Percentage error:
\[\lambda=\frac{D_{m+n}^{2}D_{m+n}^{2}}{4nR}………(iii)\]
Therefore the maximum proportional error in λ is
\[\frac{\partial \lambda}{\lambda}=\frac{\delta(D_{m+n}^{2}D_{m}^{2})}{D_{m+n}^{2}D_{m}^{2}}
\]
The error in is 4 x v.c. and hence the maximum error in \[{D_{m+n}^{2}D_{m}^{2}}\] is8 x v.c.
Hence the maximum percentage error is \( dλ/λ \) x 100%.