91Ó°ÊÓ

A laser beam is a single-wavelength stream of concentrated, coherent light.

Setting the derivative of the following equation to zero and solving the resultant equation will reveal the position of the first and second secondary maxima.

$I_{\text{slit}}=I_0{\left[\frac{\sin (\mathrm{π}ay/\mathrm{λ}L)}{\mathrm{π}ay/\mathrm{λ}L}\right]}^2$

where the first maximum's position is judged to be

$y_{\max ,1}=1.43\left(\frac{\mathrm{λ}L}{a}\right)$

We can use this equation to find the value of the term$\left(\frac{\mathrm{λ}L}{a}\right)$; note that we don't need to know the values of$a$, $\mathrm{λ}$or$L$individually; instead, we can use this equation,

You only need to understand $\left(\frac{\mathrm{λ}L}{a}\right)$, and you'll see why in a minute.

$$\begin{gathered} \frac{\mathrm{λ}L}{a}=\frac{y_{\max ,1}}{1.43} \\ =\frac{26\mathrm{mm}}{1.43} \\ =18.2\mathrm{mm} \end{gathered}$$

The following reaction now describes the position of the initial minimum.

$y_p=\frac{p\mathrm{λ}L}{a}p=1,2,3,…$

We have the value of $\frac{\mathrm{λ}L}{a}$, and$p=1$. Hence

$$\begin{gathered} y_1=\frac{\mathrm{λ}L}{a} \\ =18.2\mathrm{mm} \end{gathered}$$