## THEORY

The arrangement for the determination of wavelength of light is shown in the figure below. A parallel beam of light from the lens L, is reflected by the glass plate B inclined at angle of 45° to the horizontal, L is a plano-convex lens of large focal length. Newton’s rings are viewed through B by the traveling microscope M focused on the air film circular bright and dark rings are seen with the center dark. With the help of a traveling Microscope, the diameter is measured for the nth dark ring.

Suppose the diameter of nth ring = Dn

r²n = nλR

but, rn = Dn/2

D^{2}n = 4nλR …………. (i)

The diameter of the (n+m)dark rings is Measured. Let it be Dn+m, Therefore, D^{2}n+m =4(n+m)λR……………(ii)

Substrating (i) from (ii)

D^{2}n+m-D^{2}n = 4(n+m)λR – 4nλR

D^{2}n+m-D^{2}n = 4nλR +4mλR -4nλR

D^{2}n+m-D^{2}n = 4mλR

λ = D^{2}n+m-D^{2}n/4mR ………….(iii)

λ = D^{2}n+m-D^{2}n/4mR

Where

R = Radius of curvature of the surface of lens in content with the glass plate and

Dn = Diameter of nth dark or bright fringes

Dm = Diameter of mth dark or bright fringes

R= l^{2}/6h +h/2

## OBSERVATION

l =29mm

h = 0.19mm

R = (29×10^{-3})^{2}/6X0.19X10^{3} + 0.19X10^{3}/2

= 0.68m

No. of rings | Microscope ReadingLeft (M.S) | Microscope ReadingLeft (C.S) | Microscope ReadingLeft (Total) | Microscope Reading diameter (mm)Right (M.S) | Microscope Reading diameter (mm)right (C.S) | Microscope Reading diameter (mm)right (total) | |

20 | 49 | 50 | 49.5 | 43 | 53 | 43.53 | 5.93 |

16 | 49 | 83 | 49.83 | 44 | 89 | 44.89 | 4.94 |

12 | 48 | 54 | 48.54 | 44 | 23 | 44.23 | 4.31 |

8 | 48 | 67 | 48.67 | 45 | 0.4 | 45.04 | 3.63 |

4 | 48 | 18 | 48.18 | 45 | 59 | 45.59 | 2.59 |

(m,n) | ( D^{2}n- D^{2}m) (10^{-6}m^{2}) | λ = D^{2}n- D^{2}m/4R(n-m) (10^{-7}m) |

(12,16) | 5.8275×10^{-6}m^{2} | 5.356×10^{-7}m |

(12,8) | 5.3992×10^{-6}m^{2} | 4.9×110^{-7}m |

(8,4) | 6.4688×10^{-6}m^{2} | 5.946×10^{-7}m |

(20,16) | 10.76×10^{-6}m^{2} | 9.8×10^{-7}m |

## CALCULATION

Mean of wavelength (λ)= (5.356 +4.9 +5.946 +9.8)X10^{–}7 / 4

= 26/4 x10^{-7}m

= 6.5×10^{-7}m

**ERROR**= (Standard value – Observed value)/Standard value x 100%

= (5890-6500 / 5890 x 100)

= 610 X 100 / 5890

= 10.356%

## RESULT

The wavelength of given sodium light by using Newton’s ring is found to be 6.5X10^{-7}m with error 10.356%

## PRECAUTIONS

i) A lens and glass plate should be cleaned.

ii) A lens of Large Radius of curvature preferable plane convex should be used.