Question

How many diffraction maxima are contained in a region of the Fraunhofer single-slit pattern, subtending an angle of 2.12°, for a slit width of 0.110 mm, using light of wavelength 582 nm?

Answer 1

Answer:

6

Explanation:

We are given that

$\theta=2.12^{\circ}$

Slid width,a=0.110 mm=$0.11\times 10^{-3} m$

$1mm=10^{-3} m$

Wavelength,$\lambda=582 nm=582\times 10^{-9}$ m

$1nm=10^{-9} m$

We have to find the number of diffraction maxima are contained in a region of the Fraunhofer single-slit pattern.

$asin\theta=\frac{2N+1}{2}\lambda$

Using the formula

$0.11\times 10^{-3}sin(2.12)=\frac{2N+1}{2}(582\times 10^{-9})$

$2N+1=\frac{0.11\times 10^{-3}sin(2.12)\times 2}{582\times 10^{-9}}$

$2N+1=13.98$

$2N=13.98-1=12.98$

$N=\frac{12.98}{2}\approx 6$

Hence, 6 diffraction maxima are contained in a region of the Fraunhofer single-slit pattern