Light from a helium-neon laser falls on two narrow slits with separation 0.200 mm.On a screen 1.00 m away from the double-slits an interference pattern emerges.If the fifth maximum is detected at 1.58 cm distance from the center,what is the wavelength of the light?

Question

Quizplus · Accepted Answer

We can use the formula for the grating spacing:

d sinθ = mλ

where d is the distance between the slits (0.2 mm), θ is the angle between the line connecting the center of the double slits and the center of the corresponding bright fringe on the screen, m is the order of the maximum (5), and λ is the wavelength of the light.

We can first use trigonometry to find θ:

tan θ = opposite/adjacent = 1.58 cm/1 m 
θ = arctan(1.58 cm/1 m) = 0.924 radians

Then we can solve for λ:

d sinθ = mλ 
λ = d sinθ / m = (0.2 mm)(sin 0.924) / 5 
λ = 0.632 nm

So the answer is C) 632 nm.

Light from a Helium-Neon Laser Falls on Two Narrow Slits