Index of Refraction Problems

Category: Physics

"Published in Newark, California, USA"

A ray of light strikes a water surface at an angle of incidence of 40°. What is the angle of refraction in the water? 

Solution:

The given problem is about refraction of light in which the speed of light will change as it passes through the material. There's a bending of ray of light also in the material. To illustrate the problem, it is better to draw the figure as follows

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According to Snell's Law, the index of refraction is inversely proportional to angle of refraction. The higher the value of index of refraction, the smaller the angle of refraction is. 

From the Table of Index of Refraction, the index of refraction of air at 20°C is 1.000 and water at 20°C is 1.333. Therefore, the angle of refraction in the water is

Take the inverse sine on both sides of the equation, we have

                               or

Inclined Plane Problems, 3

Category: Mechanics, Physics

"Published in Newark, California, USA"

The block shown in the figure is acted on by its weight W = 400 lbs., a horizontal force F = 600 lbs., and the pressure P exerted by the inclined plane. The resultant R of these forces is parallel to the incline. Determine P and R. Does the block move up or down the incline?

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Solution:

The first thing that we need to do is to get the x and y components of each forces and then isolate the given figure as follows 

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Since we don't know the direction of the resultant, let's assume that the direction is upward because the value of F is greater than the weight of a block. 

The sum of x component is

The sum of y component is

Substitute the value of P to the first equation. Therefore, the value of R is

Since the value of R is positive, then the block is moving upward the incline. 
 

Resultant of Forces and Components, 2

Category: Mechanics, Physics

"Published in Newark, California, USA"

The force system as shown in the figure has a resultant of 200 lbs. pointing up along the y axis. Compute the values of F and θ required to give this resultant.

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Solution:

The first thing that we need to do is to get the x and y components of each forces and then isolate the given figure as follows

Photo by Math Principles in Everyday Life

The sum of y components is

The sum of x components is

 

 

 

 

Divide the first equation by the second equation in order to solve for θ, we have
 

Take the inverse tangent on both sides on the equation, we have

                                or

Substitute the value of θ to either of the two working equations, we have