Coherent light that contains two wavelengths, 660 nm (red) and 470 nm (blue), passes through two narrow slits that are separated by 0.310 mm. Their interference pattern is observed on a screen 4.40 m from the slits. What is the disatnce on the screen between the first order bright fringe for each wavelength?

0.002699 m or 2.699 mm

Explanation:

y = Fringe distance

d= Distance between slits = 0.310mm

L = Screen distance = 4.40m

λ= Wavelength

Given from question

λ₁= 660 nm = 6.6 x 10^-9 m

λ₂= 470 nm = 4.7 x 10^-9 m

d = 0.340 mm = 3.4 x 10^-3 m

L = 4.40 m

In the case of constructive interference, we use below formula

y/L = mλ/d

For first order wavelength

(y₁/4.40) =(1×660x10⁻⁹)/(0.310*10⁻³)

y₁= (0.310*10⁻³)×(4.40)/(0.310*10⁻³)

y₁=0.00937m

(y2/4.40) =(1×470x10⁻⁹)/(0.310*10⁻³)

y2= =(1×470x10⁻⁹)×(4.40)/(0.310*10⁻³)

y2=0.00667m

distance between the fringes is given by (y₁ -y2)

=0.00937-0.00667=0.002699m

Therefore, distance on the screen between the first-order bright fringes for the two wavelengths is 0.002699 m or 2.699 mm

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