Question

The plane wavefront shown in the diagram is travelling from air to water. $LM$ is the incident wavefront and $L^{\prime }{M}^{\prime }$ is the refracted wavefront. The wavefront $LM$ is obliquely incident on the surface of water at an angle of incidence ${60}^{\circ }$. If the distance $M{M}^{\prime }=10\text{cm}$, find distance $L{L}^{\prime }$. Take refractive index of water equal to $\frac{4}{3}$.

• A. $30\text{cm}$
• B. $40\text{cm}$
• C. $13.33\text{cm}$
• D. $7.5\text{cm}$

Answer 1

The correct option is D $7.5\text{cm}$


As $LM$ and $L^{\prime }{M}^{\prime }$ are the incident and refracted wavefronts respectively, the distances $M{M}^{\prime }$ and $L{L}^{\prime }$ are covered by the rays of light in the same interval of time.
$\therefore$ We can write, $M{M}^{\prime }=c_{a}t$ and $L{L}^{\prime }=c_{w}t$

Now, ${\mu }_w=\frac{c_a}{c_w}=\frac{M{M}^{\prime }}{L{L}^{\prime }}$

$\Rightarrow \frac{4}{3}=\frac{10}{L{L}^{\prime }}$

$\therefore L{L}^{\prime }=7.5\text{cm}$

Hence, $\left(D\right)$ is the correct answer.