Question

In a single-slit diffraction pattern on a flat screen, the central bright fringe is 0.9 cm wide when the slit width is 4.80 10-5 m. When the slit is replaced by a second slit, the wavelength of the light and the distance to the screen remaining unchanged, the central bright fringe broadens to a width of 2.1 cm. What is the width of the second slit? It may be assumed that θ is so small that sin θ ≈ tan θ.

Answer 1

Slit width d= 4.8*10^-5 m

Central bright fringe Y = 0.9 cm

Distance of the edge of the central fringe to the center of thecentral fringe y = Y / 2

y= 0.45 cm

Slit width of second d ' = ?

Central bright fringe Y' = 2.1 cm

Distance of the edge of the central fringe to the center of thecentral fringe y '= Y '/ 2

y ' = 1.05 cm
we know condition for 1 st minimum is dsinθ = λ
d( y/D ) = λ
from this d α 1/ y
( d '/ d) = ( y / y ' )
from this d' = ( y / y ') * d
= (0.45/1.05)*4.8*10^-5
= 2.06* 10^-5 m