Question 24: Wave Optics

Question

A monochromatic light of wave length $6000^{\circ} \mathrm{A}$ is passed through two media A and B of thickness 10 cm and 16 cm respectively. The number of waves in $A$ is $\frac{1}{2}$ that of $B$. If the refractive index of $A$ is $\frac{4}{3}$, find the refractive index of $B$.

Accepted Answer

Let $N$ be the number of waves in a medium of thickness $d$.  Since the wavelength in a medium is $\lambda=\lambda_0/\mu$, we have
$$ N=\frac{d}{\lambda}=\frac{d\,\mu}{\lambda_0}\,. $$
For medium A:
$$    N_A=\frac{d_A\,\mu_A}{\lambda_0}       =\frac{10	ext{ cm}	imes\frac{4}{3}}{\,\lambda_0\,}.    $$
For medium B:
$$    N_B=\frac{d_B\,\mu_B}{\lambda_0}       =\frac{16	ext{ cm}	imes\mu_B}{\,\lambda_0\,}.    $$
Given $N_A=	frac12\,N_B$,
$$    \frac{10\cdot\frac{4}{3}}{\lambda_0}    =\frac12\;\frac{16\,\mu_B}{\lambda_0}    \;\;\Longrightarrow\;\;    10\cdot\frac{4}{3}    =\frac{16}{2}\,\mu_B    =8\,\mu_B.    $$
Solve for $\mu_B$:
$$    \mu_B    =\frac{10\cdot\frac{4}{3}}{8}    =\frac{40}{3\cdot8}    =\frac{40}{24}    =\frac{5}{3}\,.    $$
Answer: $\displaystyle \mu_B=	frac{5}{3}$  (Option D).

Answer

$\mu_B=\frac{4}{3}$

Answer

$\mu_B=\frac{3}{5}$

Answer

$\mu_B=\frac{3}{2}$

Answer

$\mu_B=\frac{5}{3}$

Wave Optics

A monochromatic light of wave length 6000^{\circ} \mathrm{A} is passed through two media A and B of thickness 10 cm and 16 cm respectively. The number of waves in A is \frac{1}{2} that of B. If the refractive index of A is \frac{4}{3}, find the refractive index of B.

Choose the correct answer: