Answer to Question #93208 in Optics for Lakhan Soren

Question

Compare the Fraunhofer diffraction patterns of single slit and double slits.

Answer 1

Fraunhofer diffraction is called under two conditions: an incident plane wave on an obstacle and a diffracted wave in a certain direction.

Diffraction pattern from single slit:

Intensity of wave we can calculated at formula

$$I_\phi=I_0 \frac{sin^2(\frac{b\pi}{\lambda}sin(\phi))}{(\frac{b\pi}{\lambda}sin(\phi))^2}$$

Conditions of maximums and minimums of intensity

1)The main maximum

$$sin(\phi)=0$$

2)Maximum of the first, second and other orders

$$sin(\phi_1)=\pm1.43\cdot \frac{\lambda}{b}$$ $$sin(\phi_2)=\pm2.46\cdot \frac{\lambda}{b}$$

3)Minimums m-orders

$$sin(\phi)=\pm m\frac{\lambda}{b}, m=1,2,3,...$$

Diffraction pattern for two slit:

The position of the diffraction maximum and minimum from one slit does not depend on its position, but is determined by the direction of the diffracted rays. This means that moving the slit parallel to itself does not lead to a change in the diffraction pattern. Consequently, the pictures created by each slot individually will be exactly the same.

The resulting picture can be determined by adding these two pictures, taking into account the interference of coherent waves coming from each of the slots.

The condition of minimum intensity is also satisfied in this case. In addition, directions are possible in which the vibrations sent by the two slots cancel each other out. There are additional lows. They will be observed in those directions to which the difference in stroke corresponds.

$$\frac{1}{2}\lambda, \frac{3}{2}\lambda, \frac{(2m+1)}{2}\lambda,$$

The dashed curve shows the intensity distribution from one slit.