Question

You illuminate a slit with a width of 70.3 μm with a light of wavelength 719 nm and observe the resulting diffraction pattern on a screen that is situated 2.11 m from the slit. What is the width, in centimeters, of the pattern?

Answer 1

4.3 cm

Step-by-step explanation:

We are given that

Width,d=70.3
`\mu m=70.3*10^(-6) m`

`1\mu m=10^(-6) m`

Wavelength,
`\lambda=719 nm=719* 10^(-9) m`

`1nm=10^(-9) m`

`r=2.11 m`

We have to find the width in cm of the pattern.

The angle for the first minimum m=1

`sin\theta_(min)\approx \theta=(\lambda)/(d)=(719* 10^(-9))/(70.3* 10^(-6))=0.0102 rad`

`y=r\theta=2.11* 0.0102=0.0215 m`

The width of the pattern=
`2y=2* 0.0215=0.043 m=0.043* 100=4.3 cm`