Question

Where $d$ is the width of the strips. Fringe visibility is defined as
A. $\dfrac{{{I_{\max }}{\text{ }} - {\text{ }}{I_{\min }}}}{{{I_{\max }}{\text{ }} + {\text{ }}{I_{\min }}}}\:$
B. $\dfrac{{{I_{\max }}{\text{ }} + {\text{ }}{I_{\min }}}}{{{I_{\max }}{\text{ }} - {\text{ }}{I_{\min }}}}\:$
C. $\dfrac{{{I_{\max }}{\text{ }} - {\text{ }}{I_{\min }}}}{{{I_{\max }}}}\:$
D. \[\dfrac{{{I_{\max }}{\text{ }} + {\text{ }}{I_{\min }}}}{{{I_{\max }}{\text{ }} + {\text{ }}{I_{\min }}}}\]\:

Answer 1

Hint:We will firstly review the definition of fringe visibility. Then we will try to connect the definition with one of the given options. Finally, we will select the correct option.The width of the strips is nothing but the width between the interferences which is also known as the band width. Different interferences are formed when different waves interfere in different ratios and thus have different intensities. The contrast of any two subsequent interference fringes.

Complete step by step answer:
Fringe visibility can be defined as the contrast between the intensities of the interference fringes. Now, from the definition of fringe visibility, we say that the formula for the fringe visibility will be a ratio between intensities. Now, the fourth option cannot be practically feasible as its ratio is directly $1$ which is not correct.

This is because the ratio being zero mathematically means that the intensities of all the interferences are always equal which is not practically possible.Now, we can make the ratio such that it is between the difference between the extreme intensities to the total of the extreme intensities. Thus, the correct formula is
 $\dfrac{{{I_{\max }}{\text{ }} - {\text{ }}{I_{\min }}}}{{{I_{\max }}{\text{ }} + {\text{ }}{I_{\min }}}}$

Hence, the correct option is A.

Note:We arrived at the answer by just connecting our basic knowledge of mathematics with the definition of fringe intensity. The other options also had the same idea behind the formula but we also used our idea of interference. It is pretty much known that the fringes lose intensities successively having maximum intensity at the central fringe.