Question

A parallel beam of light of wavelength `6000Å` gets diffracted by a single slit of width 0.3 mm. The angular position of the first minima of diffracted light is :
A. `2 xx 10^(-3)`rad
B. `3 xx 10^(-3)`rad
C. `1.8 xx 10^(-3)`rad
D. `6 xx 10^(-3)`rad

Answer 1

Correct Answer - A
Here, `lambda=6000 Ã…=6000 xx 10^(-10)m=6xx10^(-7)m`
`a=0.3mm=0.3xx10^(-3)m=3xx10^(-4)m`
For first minima, `a sin theta=lambda` where a is the slit width
`sintheta=(lambda)/(a)=(6xx10^(-7)m)/(3xx10^(-4)m)=2xx10^(-3)`
As `sin theta` is very small
` :. theta~=sintheta=2xx10^(-3)`rad