Chapter 24, Problem 4P

To determine

The fingers in the centre of the pattern on a screen $3.6m$ away.

Answer to Problem 4P

The answer is $0.039m$ .

Explanation of Solution

Given info:

Distance between the patterns,  $L=3.6m$

Distance between the slits,  $d=0.060mm=0.06\times {10}^{-3}m$

Integer,  $m=1$

Wavelength, $\lambda =656nm=656\times {10}^{-9}m$

Formula used:

It is known that $\Delta y=\frac{L\lambda \Delta m}{d}$

  $m$ is an integer

  $\lambda$ is wavelength

  $L$ is distance from slits to the screen.

  $d$ is a distance between slits

  $y$ is the distance between the fringes 

Calculation:

Substitute the values in formula $\Delta y=\frac{L\lambda \Delta m}{d}$ ,

  $\Delta y=\frac{\left(3.6\right)\left(656\times {10}^{-9}\right)\left(1\right)}{\left(0.06\times {10}^{-3}\right)}=0.039m$

Conclusion: The required value is $0.039m$ .