Question

Two waves of light in air have the same wavelength and are initially in phase. They then travel through plastic layer with thicknesses of $L_1=3.5mm$ and $L_2=5.0mm$ and indices of refraction $n_1=1.7$ and $n_2=1.25$ as shown in figure. The rays later arrive at a common point. The longest wavelength of light for which constructive interference occurs at the point is

• A. $0.8mm$
• B. $1.2mm$
• C. $1.7mm$
• D. $2.9mm$

Answer 1

Answer: (B)

$1.2mm$

Optical path travelled by wave 1, $x_1=n_1{L}_1+n_3{L}_3$

$L_3=1.5mm,n_3=1$

Optical path travelled by wave 2, $x_2=n_2{L}_2$

For wave 1 and wave 2 to interfere constructively, path difference $x_1-x_2=m\lambda$

For longest wavelength ${\lambda }_L$, $m=1$

$(1.7\times 3.5+1\times 1.5)-1.25\times 5={\lambda }_L$

Thus ${\lambda }_L=1.2mm$