Calculate the angle through which the ray has been deviated as it emerges from the plastic, given that the refractive index of plastic = 1.47.
Understand the Problem
The question requires calculating the angle of deviation of a light ray as it passes through a plastic Fresnel lens, given the refractive index of the plastic.
Answer
$1.549$
Answer for screen readers
The refractive index of the plastic is $1.549$.
Steps to Solve
- State Snell's Law
Snell's Law relates the angles of incidence and refraction to the refractive indices of the two media:
$n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$
where $n_1$ and $n_2$ are the refractive indices of the two media, and $\theta_1$ and $\theta_2$ are the angles of incidence and refraction, respectively.
- Identify Known Variables
$n_1 = 1.00$ (refractive index of air) $\theta_1 = 22.0^\circ$ (angle of incidence) $\theta_2 = 14.0^\circ$ (angle of refraction)
We are looking for $n_2$, the refractive index of the plastic.
- Solve Snell's Law for $n_2$
Rearrange Snell's Law to solve for $n_2$:
$n_2 = \frac{n_1 \sin(\theta_1)}{\sin(\theta_2)}$
- Plug in Known Values
Substitute the known values into the equation:
$n_2 = \frac{1.00 \cdot \sin(22.0^\circ)}{\sin(14.0^\circ)}$
- Calculate $n_2$
$n_2 = \frac{1.00 \cdot 0.3746}{0.2419}$ $n_2 = 1.549$
The refractive index of the plastic is $1.549$.
More Information
The refractive index is a dimensionless number that describes how light propagates through a medium. It is the ratio of the speed of light in a vacuum to the speed of light in the medium.
Tips
A common mistake is to mix up the angles of incidence and refraction, or the refractive indices. Always double-check which medium corresponds to which angle and refractive index. Also, make sure your calculator is in degree mode when calculating trigonometric functions.
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