Angle refraction from a point on glass.

In summary, the problem involves finding the angle of refraction for a ray of light passing through a rectangular block of glass surrounded by liquid carbon disulfide. The equation n2*sin(a)/n1 is used to solve for the angle of refraction, but it is a two-part problem and the angle at point A must be used to find the angle at point B.
  • #1
rcmango
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Homework Statement



The drawing shows a rectangular block of glass (n = 1.52) surrounded by liquid carbon disulfide (n = 1.63). A ray of light is incident on the glass at point A with a = 36.0° angle of incidence. At what angle of refraction does the ray leave the glass at point B?

Please explain a way to reach the solution for this problem. I tried using the equation: n2*sin(36) / n1

pic: http://img128.imageshack.us/img128/900/13113445ga1.png

Homework Equations





The Attempt at a Solution



not sure why this would not work: sin(B) = n1/n2 * sin(a)

so, 1.63/1/52 * sin(36) comes to 39.1 degrees??

please correct me if this is incorrect. However, the answer doesn't seem to be accurate. This is the angle that is refracted from the glass at B correct?

thanks.
 
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  • #2
You're using Snell's Law correctly, but I think this is a two-part problem. So first, you need to apply it to find the angle of refraction into the glass at point A. This is the angle you solved for. You need to use that angle to apply Snell's law again at point B, to find the angle at which the light leaves the glass at point B.
 
  • #3




Your approach to solving this problem is correct, but there are a few errors in your calculations. Let's break down the steps to reach the correct solution.

1. First, we need to understand the relationship between the angles of incidence and refraction in a situation like this. According to Snell's law, the ratio of the sines of these two angles is equal to the ratio of the refractive indices of the two materials. This can be expressed as:

sin(θ1) / sin(θ2) = n2 / n1

Where θ1 is the angle of incidence, θ2 is the angle of refraction, n1 is the refractive index of the first material (in this case, glass), and n2 is the refractive index of the second material (carbon disulfide).

2. Next, we need to rearrange this equation to solve for θ2, the angle of refraction. This can be done by cross-multiplying and taking the inverse sine of both sides:

sin(θ2) = n1/n2 * sin(θ1)

3. Now, we can plug in the values given in the problem to find the angle of refraction. Remember to convert the angle of incidence from degrees to radians before calculating the sine. This gives us:

sin(θ2) = 1.52/1.63 * sin(36°)

sin(θ2) = 0.931 * 0.588

sin(θ2) = 0.548

θ2 = sin^-1(0.548)

θ2 = 33.7°

Therefore, the ray of light will leave the glass at point B at an angle of 33.7°.

4. It's always a good idea to check our answer by using the inverse cosine function to calculate the angle of incidence from the given values. This should give us the same angle we started with (36°). Let's see:

sin(θ1) = n2/n1 * sin(θ2)

sin(θ1) = 1.63/1.52 * sin(33.7°)

sin(θ1) = 1.072 * 0.583

sin(θ1) = 0.625

θ1 = sin^-1(0.625)

θ1 = 37.9°

As you can see, the angle of
 

Related to Angle refraction from a point on glass.

1. What is angle refraction from a point on glass?

Angle refraction from a point on glass is the change in direction of a light ray as it passes through a glass surface. This change in direction is caused by the difference in the speed of light in air versus the speed of light in glass.

2. How is angle refraction calculated?

Angle refraction is calculated using Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speeds of light in the two mediums.

3. What factors affect angle refraction from a point on glass?

The factors that affect angle refraction from a point on glass include the angle of incidence, the refractive index of the glass, and the wavelength of the light. The temperature and pressure of the glass can also have a small effect on angle refraction.

4. How does angle refraction affect the appearance of objects through glass?

Angle refraction can cause objects to appear shifted or distorted when viewed through glass. This is because the light rays passing through the glass are bent, changing the apparent position of the object.

5. Why is angle refraction important in optics and engineering?

Angle refraction is important in optics and engineering because it allows for the design and creation of lenses, prisms, and other optical instruments. It also plays a crucial role in understanding the behavior of light and how it interacts with different materials.

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