University Physics Volume 3 - 1.3 Refraction - EXAMPLE 1.2

EXAMPLE 1.2
Determining the Index of Refraction

Find the index of refraction for medium 2 in Figure (a), assuming medium 1 is air
and given that the incident angle is
°
and the angle of refraction is
°.

You can change angles and the result will be calculated for your angles.

Strategy
The index of refraction for air is taken to be 1 in most cases (and up to four significant figures, it is 1.000). Thus, n₁ = 1.00 here. From the given information, θ₁ = 30.0° and θ₂ = 22.0°.
With this information, the only unknown in Snell’s law is n₂, so we can use Snell’s law to find it.

Solution
From Snell’s law, we have
n₁ sin θ₁ = n₂ sin θ₂

n₂ = n₁ sinθ₁ / sinθ₂.
Entering known values,
n₂ = 1.00 sin 30.0° / sin 22.0° = 0.500 / 0.375 = 1.33

What is C?

The angular frequency of the oscillations in an LC circuit is .0×10³ rad/s.

If L= H, what is C?

Solution:

C=µC

What is the maximum current flowing through the circuit?

In an LC circuit, the self-inductance is
L=.0×10⁻² H
and the capacitance is
C=.0×10⁻⁶ F.

At t=0, all of the energy is stored in the capacitor, which has a charge
q=×10⁻⁵ C. 

(a) What is the angular frequency ω of the oscillations in the circuit?

(b) What is the maximum current I₀ flowing through the circuit?

(c) How long does it take the capacitor to become completely discharged? t_d=?

(d) What is the capacitor charge in µC when time t = ×10⁻⁴s?

Solution:

(b) The current is at its maximum when all the energy is stored in the inductor. From the law of energy conservation:


(c) The capacitor becomes completely discharged in one-fourth of a cycle, or during a time T/4, where T is the period of the oscillations. Since

(d) q=q₀ × cos(ω t)



 ω= rad/s
  I₀= A
t_d= s
q(t)= µC

LC Angular Frequency of the Oscillations in the Circuit

In an LC circuit, the self-inductance is
L=.0×10⁻² H
and the capacitance is
C=.0×10⁻⁶ F.

At t=0, all of the energy is stored in the capacitor, which has a charge
q=×10⁻⁵ C. 

What is the angular frequency of the oscillations in the circuit?

 ω= rad/s

Problem-Solving Strategy

 When you are solving some physical problem, try to write your solution in the form of one symbolic equation, where on the left you have the symbol of an unknown physical parameter that you have to calculate, and on the right, you have symbols of only known physical parameters and known constants. Only after this step should you make substitutions on the right, replacing symbols with physical values. If you are doing multi-step calculations using intermediate calculations, write and use intermediate calculations with as many significant figures as possible.

But enter the final result using the correct number of significant figures after rounding the calculated final value. Rounding off in intermediate calculations often makes the final result incorrect. Before you enter the final result, check again what the units of the final results should be according to the text of the problem. The test system accepts as correct results only numbers obtained in expressions written in these units.