Question

A beam of light striking the surface of a glass plate from the air as shown in above figure.
If the angle between reflected beam and refracted beam is 90 degree, Find out the refractive index of the glass?

• A. $\sin {55}^o$
• B. $\frac{1}{\sin {55}^o}$
• C. $\frac{1}{\sin {35}^o}$
• D. $\frac{\sin {55}^o}{\sin {35}^o}$
• E. $\frac{\sin {35}^o}{\sin {55}^o}$

Answer 1

Answer: (D)

$\frac{\sin {55}^o}{\sin {35}^o}$

According to figure, ${\theta }_1+{35}^o={90}^o$ $⟹{\theta }_1={55}^o$

As the angle of incidence is equal to angle of reflection, thus ${\theta }_2={\theta }_1={55}^o$

Also ${\theta }_3={90}^o-{\theta }_2={90}^o-{55}^o={35}^o$

Given : ${\theta }_3+{\theta }_4={90}^o$

$\therefore$ ${\theta }_4={90}^o-{35}^o={55}^o$

$⟹$ ${\theta }_5={90}^o-{\theta }_4={90}^o-{55}^o={35}^o$

Using Snell's law of refraction : $n_a\times sin{\theta }_1=n_g\times sin{\theta }_5$ where $n_a=1$

$\therefore$ $1\times sin{55}^o=n_g\times sin{35}^o$ $⟹n_g=\frac{sin{55}^o}{sin{35}^o}$