Question

Problem 59

Answer 1

Given information

Number of fringes shifted from the central reference line,n=158

Wavelength of incident light =632.8nm

Length of cavity=1.155cm

 

Step-by-step explanation

Step 1.

In Michelson interferometer, for constructive interference, path difference between two reflected rays is given as

      ..............(1)

here,  

m- is number of fringes shifted from the central reference line

Here    is wavelength of incident light and n  represents number of fringes

When gas of refractive index n is filled inside the glass that time wavelength of light ray coming out of the glass will be

 

Condition for destructive interference is given as,

 

  ....................(2)    

due to one dark fringe shift path changes by length of   If the cavity has a length L, then  number of wavelengths in vacuum will be    and number of  wavelength with the gas present is  

Difference in the number of wavelengths in the two media is given as 

   

Since, in the cavity light ray travel twice, therefore number of dark fringe shifts is equal to twice of difference in the number of wavelengths in  two media. 

 

   

   ...................(1)