Chapter 24, Problem 15P

To determine

The angle between the two refracted beams.

Answer to Problem 15P

  $0.22°$

Explanation of Solution

Given info:

The angle made by a beam while striking a piece of glass, ${\theta }_1=60°$

First value of refractive index of the glass $n_1=1.4820$

Second value refractive index of the glass $n_2{}^{\text{'}}=1.4742$

Formula used:

The angles of refraction in the glass: $n_{1}sin{\theta }_1=n_{2}sin{\theta }_2$

Where,

  $n_1$ is Refractive index of first medium

  $n_2$ is Refractive index of second medium

  ${\theta }_1$ is angle of incidence

  ${\theta }_2$ is angle at which light transmitted to another medium.

Calculation:

Calculation for the angles of refraction in the glass for the first case is: $n_{1}sin{\theta }_1=n_{2}sin{\theta }_2$ . Where, ${\theta }_2$ is angle of refraction in the glass, $n_1=1$ is Refractive index of air.

Now, substitute the give values:

  $\left(1.00\right)sin\left(60.00°\right)=\left(1.4820\right)sin{\theta }_2$

  ${\theta }_2=35.76°$

Calculation for the angles of refraction in the glass for the first case is: $n_{1}sin{\theta }_1=n_2{}^{\text{'}}sin{\theta }_2{}^{\text{'}}$ . Where, ${\theta }_2{}^{\text{'}}$ is angle of refraction in the glass, $n_1=1$ is Refractive index of air.

Now, substitute the give values:

  $\left(1.00\right)sin\left(60.00°\right)=\left(1.4742\right)sin{\theta }_2$

  ${\theta }_2=35.98°$

Calculation for angle between the refracted beams: ${\theta }_2{}^{\text{'}}-{\theta }_2$

  $=35.98°-35.76°$

  $=0.22°$

Conclusion: The required angle is $0.22°$ .