4. Monochromatic light incident on a slit of width 0.050 mm forms a diffraction pattern on a screen 2.0 m away.The second-order dark fringe is observed at an angle of 1.56^circ . Calculate the wavelength of the light.

Question

4. Monochromatic light incident on a slit of width 0.050 mm forms a diffraction pattern on a screen 2.0 m away.The second-order dark fringe is observed at an angle of 1.56^circ . Calculate the wavelength of the light.

Answer 1

Here's how to calculate the wavelength of the light:**1. Understand the concept:**This problem involves single-slit diffraction. The condition for dark fringes (destructive interference) in a single-slit diffraction pattern is given by:* *a*sin(θ) = *mλ*Where:* *a* is the width of the slit* θ is the angle of the dark fringe relative to the central maximum* *m* is the order of the dark fringe (an integer, m = 1, 2, 3, ...)* λ is the wavelength of the light**2. Gather the given information:*** *a* = 0.050 mm = 0.050 x 10⁻³ m (Convert to meters)* θ = 1.56°* *m* = 2 (second-order dark fringe)**3. Solve for λ:**Rearrange the formula to solve for the wavelength:* λ = *a*sin(θ) / *m*Substitute the given values:* λ = (0.050 x 10⁻³ m) * sin(1.56°) / 2* λ ≈ (0.050 x 10⁻³ m) * 0.0272 / 2* λ ≈ 6.8 x 10⁻⁷ m**4. Express the answer in appropriate units:**The wavelength is typically expressed in nanometers (nm).* λ ≈ 680 nm**Therefore, the wavelength of the light is approximately 680 nm.**

Question

4. Monochromatic light incident on a slit of width 0.050 mm forms a diffraction pattern on a screen 2.0 m away.The second-order dark fringe is observed at an angle of 1.56^circ . Calculate the wavelength of the light.

Solution

Answer