A ray of light goes from water (nwater=1.333) into ice (nice=1.309).
Which of the following statements is true?
1) The ray gets closer to the normal after crossing the interface.
2) The ray does not change directions after crossing the interface.
3)The ray gets farther away from the normal after crossing the interface.
4)There is not enough information. The incident angle is needed.
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go to lecture
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going from higher to lower refractive index so away from normal
To determine which statement is true, we need to understand the behavior of light when it crosses the interface between two different mediums.
When light goes from one medium to another, it changes direction. This phenomenon is known as refraction. The change in direction occurs because light travels at different speeds in different mediums.
The behavior of light during refraction can be explained using Snell's law, which states:
n1 * sin(θ1) = n2 * sin(θ2)
where n1 and n2 are the refractive indices of the two mediums, and θ1 and θ2 are the angles that the incident ray and refracted ray make with the normal to the interface.
In this case, the incident ray is traveling from water to ice. The refractive index of water (nwater) is 1.333, and the refractive index of ice (nice) is 1.309.
To determine which of the given statements is true, we need to compare the angles of the incident and refracted rays.
1) The ray gets closer to the normal after crossing the interface.
If this statement is true, it means that the angle of the refracted ray (θ2) is smaller than the angle of the incident ray (θ1). According to Snell's law, this would imply that n1*sin(θ1) > n2*sin(θ2). However, since we have n1 > n2 (1.333 > 1.309), this statement is incorrect.
2) The ray does not change directions after crossing the interface.
This statement implies that the angle of the refracted ray (θ2) is the same as the angle of the incident ray (θ1). However, Snell's law tells us that this can only be true if n1*sin(θ1) = n2*sin(θ2). Since the refractive indices are different in this case (1.333 ≠ 1.309), the angles of the incident and refracted rays cannot be equal. Therefore, this statement is also incorrect.
3) The ray gets farther away from the normal after crossing the interface.
If this statement is true, it means that the angle of the refracted ray (θ2) is larger than the angle of the incident ray (θ1). In terms of Snell's law, this would imply that n1*sin(θ1) < n2*sin(θ2). Given that n1 > n2 (1.333 > 1.309), this statement is true.
4) There is not enough information. The incident angle is needed.
While it is true that the incident angle affects the behavior of light during refraction, we can still determine the validity of the given statements without knowing the exact incident angle. Snell's law provides a general relationship between the angles and refractive indices involved, allowing us to make conclusions based on the refractive indices of the two mediums.
Based on this analysis, the correct statement is: The ray gets farther away from the normal after crossing the interface (statement 3).