Question:

A double-slit experiment is performed using light of wavelength λ = 600 nm. The distance between the double slits is d = 0.2 mm. The interference pattern on a screen is observed at a distance D = 2 m from the double slits. The first-order bright fringe is observed at an angle θ = 0.02 radians from the central maximum.

a) Calculate the distance between adjacent bright fringes. b) Determine the width of each bright fringe. c) If the separation between the slits is increased, will the width of the bright fringes increase or decrease? Justify your answer. d) If the wavelength of the light is reduced, will the distance between adjacent bright fringes increase or decrease? Justify your answer.

Answer:

a) The distance between adjacent bright fringes can be calculated using the formula:

d_y = λD / d

where d_y is the distance between adjacent bright fringes, λ is the wavelength of light, D is the distance of the screen from the double slits, and d is the distance between the double slits.

Plugging in the given values:

d_y = (600 nm) * (2 m) / (0.2 mm)
    = (600 * 10^-9 m) * (2 m) / (0.2 * 10^-3 m)
    = 6 * 10^-4 m = 0.6 mm

Therefore, the distance between adjacent bright fringes is 0.6 mm.

b) The width of each bright fringe can be calculated using the formula:

w = λD / d

where w is the width of each bright fringe. Using the given values:

w = (600 nm) * (2 m) / (0.2 mm)
  = (600 * 10^-9 m) * (2 m) / (0.2 * 10^-3 m)
  = 6 * 10^-4 m = 0.6 mm

Therefore, the width of each bright fringe is 0.6 mm.

c) If the separation between the slits is increased, the width of the bright fringes will decrease. This can be understood by considering the equation for fringe width:

w = λD / d

As the separation d between the slits increases, the value of w decreases. This means that the width of each bright fringe becomes narrower.

d) If the wavelength of the light is reduced, the distance between adjacent bright fringes will decrease. This can be understood by considering the equation for the distance between adjacent bright fringes:

d_y = λD / d

As the wavelength λ decreases, the value of d_y decreases. This means that the distance between adjacent fringes becomes shorter.