Q46P - University Physics with Modern Physics

Question

Coherent monochromatic light of wavelength $\mathit{\lambda }$passes through a narrow slit of width a, and a diffraction pattern is observed on a screen that is a distance x from the slit. On the screen, the width w of the central diffraction maximum is twice the distance x. What is the ratio a/$\mathit{\lambda }$of the width of the slit to the wavelength of the light?

Step-by-Step Solution

Answer

The ratio of the width of the slit to the wavelength of the light 

Step 1: Central maximum

The separation between the two first-order (m=1, -1) minima, i.e., dark lines, is the width w of the central maximum. As a result, the distance between the center of the central maximum and the first dark line is w/2. if the first dark line intersects the central maximum at an angle 

The equation is;

                                 

Step 2: Ratio of the width of the slit to the wavelength of the light

The distance between the slit and the screen x=w/2;

Therefore,  

Hence, the ratio of the width of the slit to the wavelength of the light