Question

A beam of light passes through a sheet of plastic and out into the air. The beam makes ${\theta }_1$ angles with the normal as it passes through the plastic and the angle the beam of light makes with the normal as it passes into the air is ${\theta }_2$. The refractive index for air is $1$ and The refractive index for plastic is $2$.
Calculate the value of $\sin {\theta }_2$, in terms of ${\theta }_1$?

• A. $\frac{1}{2}\sin {\theta }_1$
• B. $2\sin {\theta }_1$
• C. $\sin 2{\theta }_1$
• D. $\sin \frac{1}{2}{\theta }_1$
• E. $4\sin {\theta }_1$

Answer 1

The correct option is B $2\sin {\theta }_1$

Given - angle of incidence $i={\theta }_1$ , angle of refraction ${\theta }_2$ ,refractive index of first medium ${\mu }_1=2$ , refractive index od second medium ${\mu }_2=1$

by snell's law

$\sin i/\sin r={\mu }_2/{\mu }_1$

$\sin {\theta }_1/\sin {\theta }_2=1/2$

or $\sin {\theta }_2=2\sin {\theta }_1$