Question

When a light of wavelength $4000$ $\stackrel{\circ }{A}$ in vacuum travels through the same thickness in diamond and water separately, the difference in the number of waves is $200$. Find the thickness, if refractive indices of diamond and water are $\frac{5}{2}$ and $\frac{4}{3}$ respectively.

• A. $0.685mm$
• B. $0.0685mm$
• C. $68.5mm$
• D. $6.85mm$

Answer 1

The correct option is B $0.0685mm$

The given information means that the phase difference is $400\pi$

Hence, $(\frac{2\pi }{{\lambda }_1}-\frac{2\pi }{{\lambda }_2})t=\varphi$

Since ${\lambda }^{\prime }=\frac{\lambda }{\mu }$,

$(\frac{2\pi }{1600}-\frac{2\pi }{3000})t=400\pi$

$\frac{7}{24000}t=200$

Hence $t=685714.28\stackrel{\circ }{A}=0.0685mm$