Question

A ray of light travels from air to glass at an angle of incidence of ${37^ \circ }$, the angle of refraction is ${24^ \circ }$. What is the refractive index of glass? (Given: $\sin {37^ \circ } = 0.60$, $\sin {40^ \circ } = 0.40$)
A. 0.66
B. 0.133
C. 1.5
D. None

Answer 1

Hint: Glass is a denser medium and air is a rarer medium, therefore when light ray travels from air to glass then the refracted ray bends towards the normal. Refractive index of glass can be calculated from Snell’s law which is the ratio of sine of angle of incidence to sine of angle of refraction.

Complete step by step answer:
We are given to find the refractive index of glass when a ray of light travels from air to glass at an angle of incidence of ${37^ \circ }$, the angle of refraction is ${24^ \circ }$.

Snell’s law is used to describe the relationship between angle of incidence and angle of refraction. It states that the ratio of the sine of angle of incidence to the sine of angle of refraction is always a constant. And this constant is called a refractive index.
${n_1}\sin i = {n_2}\sin r$, ${n_1}$ is the refractive index of air and ${n_2}$ is the refractive index of glass, refractive index of air is 1.
The angle of incidence is the angle between incident ray and the normal represented using ‘i’; the angle of refraction is the angle between refracted ray and the normal represented using ‘r’.
Refractive index of the glass (${n_2}$) is the ratio of $\sin {37^ \circ }$ and $\sin {24^ \circ }$.
$
  {n_2} = \dfrac{{\sin i}}{{\sin r}} \\
  \Rightarrow {n_2} = \dfrac{{\sin {{37}^ \circ }}}{{\sin {{24}^ \circ }}} \\
  \Rightarrow {n_2} = \dfrac{{0.60}}{{0.40}} \\
  \therefore {n_2} = 1.5 \\
 $
Therefore, the correct option is Option C, 1.5.

Note: Do not confuse refraction with reflection. Where reflection happens in only one surface and refraction happens in two surfaces. For example reflection is seen in mirrors and refraction in lenses (lenses are made of two curved surfaces). Bending of light can be observed in refraction but not in reflection. Angle of incidence is the same as angle of reflection but angle of incidence is different from angle of refraction.