Question

Two narrowsslits emitting light in phase are separated by adistance of 1.0 cm. The wavelength of the light is $5.0\times {10}^{-7}$ m. The interference pattern in observed on a screen placed at a distance of 1.0 m. (a) Find the separation between the consecutive maxima. can you expect to distingish between these maxima? (b) Find the separation between the sources which will give a separation of 1.0 mm between the cnsecutive maxima.

Answer 1

Given that, $d=1cm={10}^{-2}m,$
$\lambda =5\times {10}^{-7}$ m and D = 1 m
(a) Separation between two consecutive maxima is equal to fringe to fringe width.
So, $\beta =\frac{\lambda D}{d}=\frac{5\times {10}^{-7}\times 1}{{10}^{-2}}m=5\times {10}^{-5}m=0.05mm$
(b) When, $\beta =1mm={10}^{-3}m{10}^{-3}m=\frac{5\times {110}^{-7}\times 1}{d}\Rightarrow d=5\times {10}^{-4}m=0.50mm.$