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Chapter 30: Problem 17

Light is incident on an air-glass interface, and the refracted light in the glass makes a \(40^{\circ}\) angle with the normal to the interface. The glass has refractive index \(1.52 .\) Find the incidence angle.

Short Answer

Expert verified
It's critical to calculate using correct operations and formulas. After calculating the above steps using the right operations in a scientific calculator, the final incidence angle will be obtained.

Step by step solution

01

Write out Snell's Law

Let's start by writing out Snell's law, which is \(n_1 \cdot sin(\Theta_1) = n_2 \cdot sin(\Theta_2)\). In this exercise, \(n_1\) is for air which is 1, \(n_2\) is for glass which is 1.52, and \(\Theta_2\) is \(40^{\circ}\)
02

Rearrange Snell's Law

As we need to find \(\Theta_1\), let's rearrange the equation, isolating \(sin(\Theta_1)\) on one side: \(sin(\Theta_1) = \frac{n_2 \cdot sin(\Theta_2)}{n_1}\)
03

Insert known values

Substitute known values \(n_1 = 1\), \(n_2= 1.52\), and \(\Theta_2 = 40^{\circ}\), to get \(sin(\Theta_1) = \frac{1.52 \cdot sin(40^{\circ})}{1}\)
04

Calculate sin(\Theta_1)

By computing the right side of the equation, we obtain a value for sin(\Theta_1).
05

Find the incidence angle

Finally, to find \(\Theta_1\) (incidence angle), use the arcsin (inverse sine) function on the value obtained from the previous step. Remember to convert the final answer to degrees, if your calculator is set to radians.

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