A laser beam ($\lambda$ = 694 nm) is incident on two slits 0.100 mm apart.Approximately how far apart (in m) will the bright interference fringes be on the screen 5.00 m from the double slits?
A)3.47 * 10- 3
B)3.47 * 10- 2
C)3.47 * 10 -4
D)3.47 * 10 -6
E)3.47*10 -5

Question

A laser beam ($\lambda$ = 694 nm) is incident on two slits 0.100 mm apart.Approximately how far apart (in m) will the bright interference fringes be on the screen 5.00 m from the double slits?
A)3.47 * 10- 3 
B)3.47 * 10- 2 
C)3.47 * 10 -4 
D)3.47 * 10 -6 
E)3.47*10 -5

Quizplus · Accepted Answer

The formula for the distance between bright fringes in the double-slit experiment is given by:
$$d\sin	heta = m\lambda,$$
where $d$ is the distance between the two slits, $	heta$ is the angle between the central maximum and the $m^{th}$ bright fringe, $\lambda$ is the wavelength of light, and $m$ is the order of the fringe. Taking $	heta$ to be small (corresponding to the small-angle approximation), we can use the approximation $\sin	heta \approx 	an	heta = x/L$, where $x$ is the distance from the central maximum to the $m^{th}$ bright fringe on the screen, and $L$ is the distance from the double slit to the screen. Rearranging the formula and solving for $x$, we get:
$$x = \frac{m\lambda L}{d}.$$
For the first-order bright fringe ($m=1$), we have $\lambda=694$ nm, $L=5$ m, and $d=0.1$ mm $=10^{-4}$ m. Substituting these values, we get:
$$x = \frac{(1)(694	imes10^{-9}	ext{ m})(5	ext{ m})}{10^{-4}	ext{ m}} \approx 3.47	imes10^{-3}	ext{ m}.$$
Therefore, the distance between adjacent bright fringes is approximately 3.47 mm (answer choice B).

A Laser Beam λ\lambdaλ = 694 Nm) Is Incident on Two Slits 0

A Laser Beam $\lambda$ = 694 Nm) Is Incident on Two Slits 0