Double-slit interference: Light from a 600 nm source goes through two slits 0.080 mm apart. What is the angular separation of the two first order maxima occurring on a screen 2.0 m from the slits?
A) 0.15°
B) 0.86°
C) 0.015°
D) 0.0075°
E) 1.75°

Question

Quizplus · Accepted Answer

The angular separation of the first-order maxima can be found using the equation:
$$	heta = \frac{\lambda}{d}$$
where $\lambda$ is the wavelength of the light and $d$ is the distance between the slits. Plugging in the values, we get:
$$	heta = \frac{600 	ext{ nm}}{0.080 	ext{ mm}} = 7.5 	imes 10^{-3} 	ext{ radians}$$
Now, we can use the small angle approximation $\sin{	heta} \approx 	heta$ to convert from radians to degrees:
$$	heta = 7.5 	imes 10^{-3} 	ext{ radians} \approx 0.43^\circ$$
Finally, we need to account for the fact that we are looking at the angular separation between the two first-order maxima. Since the distance between adjacent maxima is given by:
$$\sin{	heta_m} = m \frac{\lambda}{d}$$
where $m$ is an integer representing the order of the maxima, we can solve for the difference in angles between adjacent maxima, which is:
$$\Delta 	heta = \frac{\lambda}{d} = 7.5 	imes 10^{-3} 	ext{ radians} \approx 0.43^\circ$$
Therefore, the angular separation between the two first-order maxima is twice this value or:
$$\Delta 	heta_{1,2} = 2 \Delta 	heta \approx 0.86^\circ$$
So, the answer is B.

Double-Slit Interference: Light from a 600 Nm Source Goes Through