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.

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