Question

A ray of light, travelling in a medium of refractive index $\mu$, is incident at an angle i on a composite transparent plate consisting of three plates of refractive indices ${\mu }_1,{\mu }_{2}and{\mu }_3$. The ray emerges from the composite plate into a medium of refractive index ${\mu }^{,}$, at angle x, Then

• A. $sinx=sini$
• B. $sinx=\frac{\mu }{{\mu }^{,}}sini$
• C. $sinx=\frac{{\mu }^{,}}{\mu }sini$
• D. $sinx=\frac{{\mu }_1}{{\mu }_2}.\frac{{\mu }_3}{{\mu }_2}sini$

Answer 1

The correct option is B

$sinx=\frac{\mu }{{\mu }^{,}}sini$

Applying Snell's law to successive refractions, we have

$\frac{sini}{sin{r}_1}=\frac{{\mu }_1}{\mu };\frac{sin{r}_1}{sin{r}_2}=\frac{{\mu }_2}{{\mu }_1}$

$\frac{sin{r}_2}{sin{r}_3}=\frac{{\mu }_3}{{\mu }_2};\frac{sin{r}_3}{sinx}=\frac{{\mu }^{,}}{{\mu }_3}$

Multiplying these equations, we get

$\frac{sini}{sinx}=\frac{{\mu }^{,}}{\mu }Orsinx=\frac{\mu }{{\mu }^{,}}sini$