A double slit illuminated with two different colors of wavelengths 831 and 558 nm forms a two-colored diffraction pattern on a screen located 228 cm away.The slit separation is 36 wavelengths of 831 nm light.(a)What order maximum for λ = 831 nm occurs near x = 20.5 cm from zeroth order? (b)What order maximum for λ = 558 nm lies close to this order?
A)(a)3 (b)5
B)(a)6 (b)10
C)(a)2 (b)2
D)(a)5 (b)3

Question

A double slit illuminated with two different colors of wavelengths 831 and 558 nm forms a two-colored diffraction pattern on a screen located 228 cm away.The slit separation is 36 wavelengths of 831 nm light.(a)What order maximum for λ = 831 nm occurs near x = 20.5 cm from zeroth order? (b)What order maximum for λ = 558 nm lies close to this order?
A)(a)3  (b)5
B)(a)6  (b)10
C)(a)2  (b)2
D)(a)5  (b)3

Quizplus · Accepted Answer

(a) Using the formula for the position of the maxima in a double-slit diffraction pattern:

y = mλL/d

where y is the distance from the zeroth order maximum to the mth order maximum, λ is the wavelength, L is the distance from the slits to the screen, and d is the slit separation.

Plugging in the given values:

m(831 nm)(228 cm) = (36)(831 nm)

m ≈ 3

So the third order maximum for λ = 831 nm occurs at a distance of

y = (3)(831 nm)(228 cm) / (36 wavelengths)(831 nm) = 19.1 cm

which is close to x = 20.5 cm.

(b) For λ = 558 nm, using the same formula:

m(558 nm)(228 cm) = (36)(558 nm)

m ≈ 5

So the fifth order maximum for λ = 558 nm lies close to the third order maximum for λ = 831 nm.

A Double Slit Illuminated with Two Different Colors of Wavelengths