Question

When light of wavelength $4000\mathring{A}$ in vacuum travels through the same thickness in air and vacuum, the difference in the number of waves is one. Then, the thickness is (${\mu }_{air}=1.0008$ ):

• A. $0.3mm$
• B. $0.2mm$
• C. $0.5mm$
• D. $0.1mm$

Answer 1

Answer: (C)

$0.5mm$

No. of waves in vacuum $=\frac{x}{{\lambda }_{vacuum}}$
No. of waves in air $\frac{x}{\frac{{\lambda }_{vacuum}}{{\mu }_{air}}}$
Now $\frac{x}{\frac{\lambda }{{\mu }_{air}}}-\frac{x}{\lambda }=1$ (${\lambda }_{vacuum}=\lambda )$
$\frac{x}{\lambda }(\mu -1)=1$
$x=\frac{\lambda }{0.0008}$
$=0.5mm$