Chapter 24, Problem 40P

To determine

The distance of dark fringes for the given glass plates.

Answer to Problem 40P

  $1.08cm$

Explanation of Solution

Given:

Length of glass plates, $L=26.5cm$

Formula used:

Dark bands will occur when $2t=m\lambda ,m=0,1,2,\mathrm{...}$

The light rays are perpendicular to the plates, the extra path length equals $2t$ , where $t$ is the thickness of the air gap at any point.

Calculation:

There will be $24$ intervals between the $25$ dark lines This is half integer with half interval added (have $24.5$ intervals). So, between the $25$ dark lines there are $24$ intervals.

When anyone adds the half-interval at the wire end, there will be $24.5$ intervals.

Now, the separation is

  $\frac{26.5cm}{24.5\mathrm{int}ervals}=1.08cm$

Conclusion:

The required value is $1.08cm$ .