Question

Using a conventional two-slit apparatus with light of wavelength 605 nm, 34 bright fringes per centimeter are observed on a screen 3.1 m away. What is the slit separation

Answer 1

The slit separation is approximately 0.055 mm.

Step-by-step explanation:

To calculate the slit separation, we can use the formula for the distance between bright fringes in a double-slit interference pattern:

d = (λ * L) / D

where d is the distance between fringes, λ is the wavelength of light, L is the distance from the double slits to the screen, and D is the slit separation.

Substituting the given values:

d = (605 * 10-9 * 3.1) / 34

Simplifying the equation:

d = 0.000055 m = 0.055 mm

Therefore, the slit separation is approximately 0.055 mm.

Answer 2

d = 6.38 x 10⁻³ m = 6.38 mm

Step-by-step explanation:

Since, the no. of bright fringes is 34 in a centimeter, therefore, the fringe spacing must be equal to:

Fringe Spacing = Δx = 1 cm/34

Δx = 0.0294 cm = 2.94 x 10⁻⁴ m

But, the formula for fringe spacing in a double slit experiment is:

Δx = λL/d

where,

λ = wavelength of light = 605 nm = 6.05 x 10⁻⁷ m

L = Distance between screen and slits = 3.1 m

d = slit separation = ?

Therefore,

2.94 x 10⁻⁴ m = (6.05 x 10⁻⁷ m)(3.1 m)/d

d = (18.755 x 10⁻⁷ m²)/(2.94 x 10⁻⁴ m)

d = 6.38 x 10⁻³ m = 6.38 mm