How Does Light Behave When It Strikes a Glass Plate?

[kevnm67]

Homework Statement

A light ray in air is incident on a glass plate whose index of refraction is 1.42. The angle of refraction (transmitted angle) is one-half the angle of reflection. (Take the index of refraction in air to = 1.00).
A) Relative to the normal to the plate’s surface, what direction does the ray entering the glass bend?
a. toward the normal b. away from the normal c. neither

B) How is the reflected angle related to the incident angle?
a. 2 x the incident angle b. unrelated c. equal to the incident angle

C) What is the angle of refraction?
a. 37 b. 41 c. 45

Homework Equations

M=h'/h = -s'/s
1/f =1/s +1/s'

The Attempt at a Solution

I can't figure out part C and I am looking for some help.

 

[Mandeep Deka]

According to the 2nd law of reflection, the angle of incidence is equal to the angle of reflection which means that the angle of refraction is indeed half of the angle of incidence, and if you know Snell's law the problem is all yours!

 

[kevnm67]

Ok, so I do know Snells law and was thinking it should be 45...but is this the only angle it could be?

 

[Doc Al]

Ok, so I do know Snells law and was thinking it should be 45...but is this the only angle it could be?

No guessing! Set up an equation using Snell's law and solve for the angle. (You'll need a bit of trig.)

 

[kevnm67]

Ha, no exactly sure where to start without angles. My thought is since the angle of refraction is half that of the incident angle and your working within 90 degrees, 45 degrees is the only possibility?

 

[Doc Al]

Ha, no exactly sure where to start without angles. My thought is since the angle of refraction is half that of the incident angle and your working within 90 degrees, 45 degrees is the only possibility?

Call the angle of refraction θ. What would be the angle of incidence in terms of θ? Write Snell's law.

 

[kevnm67]

Call the angle of refraction θ. What would be the angle of incidence in terms of θ? Write Snell's law.

The angle of refraction is half the angle of incidence, so θ refraction is .5 θ incidence.

 

[Doc Al]

The angle of refraction is half the angle of incidence, so θ refraction is .5 θ incidence.

Write it this way: If the angle of refraction is θ, then the angle of incidence is 2θ.

Now you should be able to set up a Snell's law equation, which you can solve for θ. That might take a bit of work. (You can also just 'cheat' and plug in the answer choices--only one will satisfy the equation.)