In a double-slit interference experiment you are asked to use laser light of different wavelengths and determine the separation between adjacent maxima. You observe that this separation is greatest when you illuminate the double slit with In a double-slit interference experiment you are asked to use laser light of different wavelengths and determine the separation between adjacent maxima. You observe that this separation is greatest when you illuminate the double slit with: 1. yellow light.
2. red light.
3. blue light.
4. green light.
5. The separation is the same for all wavelengths.

we see that the lights with the most extreme wavelength are blue and red

we see that the separation between the interference lines (y) increases linearly with the wavelength for which the phenomenon is best observed in the RED response 2

Explanation:

In Young's double-slit experiment, constructive interference is written by the equation

       d sin θ = m λ

where you give the gap separation, lam the length of the donda used and m the order of interference

in many he uses trigonometry to express the synth in confusing the distances on a very distant screen

so θ = y / L

in this experiment the angles are generally very small, so

     tan θ = sin θ / cos θ = sin θ

     sint θ = y / L

let's replace

      d y / L = mλ

      y = (m L / d) λ

now let's examine the effect of changing the wavelength

1 yellow lam = 600 10⁻⁹ m

2) red lam = 750 10⁻⁹m

3) blue lam = 450 10⁻⁸ nm

4) green lam = 550 10⁻⁹ nm

we see that the lights with the most extreme wavelength are blue and red

we see that the separation between the interference lines (y) increases linearly with the wavelength for which the phenomenon is best observed in the RED response 2

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s