Question

Light with a wavelength, 1 = 682 nm forms a diffraction pattern after passing through a single-slit of width, a = 54 um. Find the angle associated with the tenth dark fringe above the central bright fringe. O A.0.569° O B.2.36° OC.7.26° O D.8.59° O E.0.1 26° QUESTION 10 How will the number of the bright lines change if the green laser will be replaced with a red laser of longer wavelength? O A The replacement will not affect the number of bright spots on the wall OB. The replacement will decrease the number of bright spots on the wall The replacement will increase the number of bright spots on the wall OC

Answer 1

(1) In Single Slit Diffraction,For Destructive interference $\small m\lambda=asin\theta$ ,where a=slit width,m=order of minimum,$\small \lambda=wavelength\,of\,light$,$\small \theta=$ angle from original direction of light to mth minima.

It is given that $\small \lambda=$ 682 nm,$\small a=54\mu m$,10th dark fringe,m=10

So $\small \theta=sin^{-1}(m\lambda/a)=sin^{-1}$ (682x10x10^-9/54x10^-6)=sin^-1(126.29x10^-3) =0.12629

$\small \theta=7.26^{\circ}$

(2) If we take maximum value of $\small sin\theta\, \, i.e. \, \, sin\theta=1$ ,then $\small m=a/\lambda$

so if we replace green laser with,red laser of longer wavelength then $\small \lambda$ increase and m decrease.

so no. of dark spots on wall will decrease,since bright spots falls between dark spots,no. of dark spots on spot will decrease.