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

6

Step-by-step explanation:

We are given that

`\theta=2.12^(\circ)`

Slid width,a=0.110 mm=
`0.11* 10^(-3) m`

`1mm=10^(-3) m`

Wavelength,
`\lambda=582 nm=582* 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=(2N+1)/(2)\lambda`

Using the formula

`0.11* 10^(-3)sin(2.12)=(2N+1)/(2)(582* 10^(-9))`

`2N+1=(0.11* 10^(-3)sin(2.12)* 2)/(582* 10^(-9))`

`2N+1=13.98`

`2N=13.98-1=12.98`

`N=(12.98)/(2)\approx 6`

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