Change of angle if refractive index changes for 10^-6

In summary, the conversation is about finding the solution for delta (ϑ), which is equal to -(minus delta n) /(n*sqrt((n^2-1))). The person asking the question is unsure about the steps involved and asks if they know how to take differentials. The other person gives an example and asks to apply the same idea to find the differentials for sin(θ) and 1/n. The first person responds that they know how to take differentials but there is no equation to differentiate, and later solves the problem with the help of the other person.
  • #1
AncientOne99
32
1
Homework Statement
The following expression sin ϑ = 1 / n applies to the angle of total reflection at the transition of the beam from glass to air. For how much
changes the angle if the refractive index changes by 10^−6?
For n take 1.5. Express the result only with n.
Relevant Equations
sin(ϑ) = 1/n(water)
Solution:
(delta (ϑ)) =
-(minus delta n) /(n*sqrt((n^2-1)))
 
Physics news on Phys.org
  • #2
If you are asking whether your answer is correct, it is.
 
  • #3
Yes i know the solution, but i don't know the steps.
 
  • #4
Do you know how to take differentials? For example
##d(x^2)=\frac{d}{dx}(x^2)dx=2xdx.##

Apply this idea to find ##d(\sin\theta)## and ##d(\frac{1}{n})## and set them equal.
 
  • #5
kuruman said:
Do you know how to take differentials? For example
##d(x^2)=\frac{d}{dx}(x^2)dx=2xdx.##

Apply this idea to find ##d(\sin\theta)## and ##d(\frac{1}{n})## and set them equal.
Yes, i know how to take the diferentials, but there is no equation to diferentiate or i don't know it.
 
  • #6
I solved it, thanks for your help !
 
  • Like
Likes kuruman

1. How does the refractive index affect the angle of refraction?

The angle of refraction is directly proportional to the refractive index. This means that as the refractive index increases, the angle of refraction also increases. Similarly, as the refractive index decreases, the angle of refraction decreases.

2. What is the relationship between the change in refractive index and the change in angle of refraction?

The change in angle of refraction is directly proportional to the change in refractive index. This means that a small change in refractive index will result in a small change in angle of refraction, while a larger change in refractive index will result in a larger change in angle of refraction.

3. Can the angle of refraction change without a change in refractive index?

No, the angle of refraction is dependent on the refractive index. Without a change in refractive index, the angle of refraction will remain constant.

4. How is the change in angle of refraction calculated when the refractive index changes by 10^-6?

The change in angle of refraction can be calculated using the formula: Δθ = (n2 - n1) * θ, where Δθ is the change in angle of refraction, n2 is the new refractive index, n1 is the original refractive index, and θ is the incident angle.

5. What factors can cause a change in refractive index?

The refractive index of a material can be affected by factors such as temperature, pressure, and the presence of impurities. Changes in these factors can lead to a change in the refractive index, which in turn affects the angle of refraction.

Similar threads

  • Introductory Physics Homework Help
Replies
3
Views
245
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
194
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
943
  • Introductory Physics Homework Help
Replies
2
Views
858
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
942
Back
Top