Chapter 19, Problem 65A

To determine

The slit width that will produce the original pattern.

Answer to Problem 65A

Slit width must be increased to $1.5w$

Explanation of Solution

Introduction:

Diffraction of light waves is the bending of light waves around the ends of an obstacle . This illuminates the region where the geometrical shadow of the obstacle is expected. As the light wave encounters the slit, the wave bends and there will be a diffraction of light waves from the slit, and the diffraction pattern can be seen on the screen which is placed far from the slit. The diffraction pattern formed by single slit contains bright and broad central band with dimmer side bands.

The angle of diffraction in single slit diffraction is depend on ratio of the wavelength of light $\left(\lambda \right)$ to slit width $\left(w\right)$ as given below,

  $\sin \theta =\frac{m\lambda }{w}$

Where $m$ is the order of diffraction.

Above equation specifies that if the light wavelength is raised to $1.5\lambda$ , the slit width must be increased to $1.5w$ to produce the original pattern.