Question

monochromatic light falls on two very narrow slits 0.044 mm apart. successive fringes on a screen 6.30 m away are 8.9 cm apart near the center of the pattern. part a determine the wavelength of the light.

Answer 1

The wavelength of the light is 6.21 × 10⁻⁷ m.

Single-slit diffraction has an equation

d sin θ = m λ

where

• d = the width of slits = 0.044 mm = 4.4 × 10⁻² mm = 4.4 × 10⁻⁵ m
• m = the orde
  Assume m = 1
• λ = the wavelength

For a small angle, sin θ = tan θ.

θ is the angle where the opposite of the angle is the width apart near the center of the pattern (x) and the adjacent is the distance between the screen from the slits (L). So $tan \: \theta = \frac{x}{L}$

• x = 8.9 cm = 8.9 × 10⁻³ m
• L = 6.30 m

d sin θ = m λ

d tan θ = m λ

$d \: \frac{x}{L} \:=\: 1 \times \lambda$

$\lambda \:=\: 4.4 \times 10^{- 5} \times \frac{8.9 \times 10^{- 2}}{6.3}$

λ = 4.4 × 10⁻⁵ × 1.41 × 10⁻²

λ = 6.21 × 10⁻⁷ m

Learn more about single-slit diffraction here: https://brainly.com/question/13151128

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