Question

How many wavelengths wide must a single slit be if, at a point 8^o from the central maximum, there is a 72 rad phase difference between the top and bottom rays?

A: 8.42

B: 12.1

C: 82.3   

D: 63.6

Answer 1

Concepts and reason

The concepts used to solve this problem are path difference and phase difference between two wavelets.

Initially, use path difference and wavelength to obtain the expression for phase difference.

Use the concept of phase difference between two wavelets to find the slit width.

Finally, use the slit width to determine the correct option.

Fundamentals

The expression for phase difference is given as follows:

Here, path difference is , phase shift is , and wavelength is .

The incorrect options are as follows:

• 8.42

• 12.1

• 63.6

The figure below shows a single fringe with a slit width .

In this figure, slit width is , angle of diffraction is , central maximum is , the point on the screen after diffraction is , and intensity of point is .

Figure represents the path difference between two waves, and this is used to find the path difference and the phase shift.

From Figure , consider The expression for the line segment is given as follows:

From Figure , the path difference is given as follows:

The line segment in Figure is .

Substitute for in the above expression.

The expression for phase difference is given as follows:

Substitute for in the above expression.

Rearrange the expression for .

Substitute for and for .

The calculated slit width is .

The calculated slit width is .

Hence, the correct option is as follows:

• .

The slit width is wavelength wide.

Ans:

The calculated slit width is .