Law of Refraction

  • Thread starter jenc305
  • Start date
  • #1
16
0
This seems really easy but I am having a really hard time getting the correct answer to this question. Any help would be much appreciated.

A ray in air is incident on a glass plate whose index of refraction is 1.60. The angle of refraction is one half the angle of reflection. The angle of refraction is closest to:

I know to use snell's law and theta_a = theta_r but the problem doesn't give me any angles to compute theta_b

(1) sin (theta_a) = 1.60 sin (theta_b)
and
theta_b = 1/2 theta_r = 1/2 theta_a
I'm I suppose to assume something here?
 

Answers and Replies

  • #2
Hootenanny
Staff Emeritus
Science Advisor
Gold Member
9,621
7
Well if you know [itex]\sin\theta_b = \frac{1}{2}\sin\theta_a[/itex], then all you need to do is a subsitution.
 
  • #3
338
11
Hootenanny said:
Well if you know [itex]\sin\theta_b = \frac{1}{2}\sin\theta_a[/itex], then all you need to do is a subsitution.

Since [tex]\theta_b=(1/2) \theta_a[/tex] then
[tex]sin\theta_a=sin(2\theta_b)=2sin\theta_b*cos\theta_b=1.6sin\theta_b[/tex]
Cancelling the sine terms:
[tex]2cos\theta_b=1.6[/tex]
etc.

-Dan
 

Related Threads on Law of Refraction

  • Last Post
Replies
2
Views
2K
Replies
1
Views
1K
  • Last Post
Replies
1
Views
5K
Replies
2
Views
1K
  • Last Post
Replies
1
Views
7K
  • Last Post
Replies
6
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
6K
  • Last Post
Replies
2
Views
3K
  • Last Post
Replies
1
Views
1K
Top