Question

Light of wavelength 578.0 nm is incident on a narrow slit. The diffraction pattern is viewed on a screen 77.5 cm from the slit. The distance on the screen between the fifth order minimum and the central maximum is 1.21 cm . What is the width of the slit in micrometers (μm)?

Answer 1

here,

the wavelength of light , lamda = 578 nm = 578 * 10^-9 m

the screen distance , D = 77.5 cm = 0.775 m

let the width of the slit in micrometers be d

the screen between the fifth order minimum and the central maximum , x = 5 * lamda * D /d

0.0121 = 5 * lamda * D /d

0.0121 = 5 * 578 * 10^-9 * 0.775 /d

solving for d

d = 185 * 10^-6 m = 185 um

the width of the slit in micrometers is 185 um