Question

Figure 35-26 shows two rays of light, of wavelength 600nm, that reflectfrom glass surfaces separated by 150nm. The rays are initially in phase.

(a) What is the path length difference of the rays?

(b) When they have cleared the reflection region, are the rays exactly in phase, exactly out of phase, or in some intermediate state?

Short answer

(a) The path length difference between the two waves is 300nm.

(b) When the rays have cleared the region, they are exactly out of phase.

Step-by-step solution

Given data: 

The wavelength of the two rays is $\lambda =600\text{nm}$
.

The thickness of the glass surface is d=300nm.

Relation between phase difference and path difference:

The phase difference between two waves of a wavelength λ having the path difference x is$\varphi =\frac{2\pi }{\lambda }x$

(a) Determining the path difference of the rays:

The upper wave travels a distance twice the thickness greater than the lower wave. Thus, the path difference is$\begin{array}{rcl}x& =& 2\times 150\text{nm}\\ & =& 300\end{array}$

Therefore, the path difference is 300nm.

Determining the phase difference of the rays:

From equation (1), the phase difference between the two waves is,$$\begin{gathered} \varphi =\frac{2\pi }{6\text{00}\text{nm}}\times \text{300}\text{nm} \\ =\frac{2\pi }{2} \\ =\pi \end{gathered}$$

Hence, the phase difference is $\pi$
.