Question

Two narrow slits $80\mathrm{\mu m}$apart are illuminated with light of wavelength localid="1649170764860" $620\mathrm{nm}$. What is the angle of thelocalid="1649170756737" $\mathrm{m}=3$bright fringe in radianslocalid="1649170769758" $?$In degreeslocalid="1649170772775" $?$

Short answer

The Angle of $\mathrm{m}=3$bright fringe in radian is$0.0225\mathrm{rad}$,in degrees $1.29°$.

Step-by-step solution

Formula for angle

For double-slit interference, the $\mathrm{m}$-th order angle is given by

${\mathrm{sin\theta }}_{\mathrm{m}}=\frac{\mathrm{m\lambda }}{\mathrm{d}}$

The distance between the slits is $\mathrm{d}$.

And the wavelength is $\mathrm{\lambda }$.

Calculation for angle

Angle is,

$\mathrm{\theta }={\sin }^{-1}\frac{\mathrm{m\lambda }}{\mathrm{d}}$

$={\sin }^{-1}\left(\frac{3·6·{10}^{-7}}{8·{10}^{-5}}\right)$

$=\sin (0.0225)$

$=0.0225\mathrm{rad}$

In degrees,

${\theta }_{deg}=\frac{2\pi }{360}·{\theta }_{\text{rad}}$

$=1.29°$

As can be seen, the small angle approximation holds to a high degree of accuracy at this angle.