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When light falls on a given plate at angle of incidence of 60º, the reflected and refracted rays are found to be normal to each other. The refractive index of the material of the plate is then
- a)0.866
- b)1.5
- c)1.732
- d)2
Correct answer is option 'C'. Can you explain this answer?
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When light falls on a given plate at angle of incidence of 60º, the r...
Given Information:
The angle of incidence is 60º, and the reflected and refracted rays are normal to each other.
Explanation:
When light passes through an interface between two media, it undergoes reflection and refraction. The angle of incidence (i) is the angle between the incident ray and the normal to the interface. The angle of reflection (r) is the angle between the reflected ray and the normal to the interface. The angle of refraction (r') is the angle between the refracted ray and the normal to the interface.
In this case, the reflected and refracted rays are normal to each other, which means the angle of reflection (r) is 90º. Let's denote the angle of refraction as r' = 90º.
Snell's Law:
Snell's law relates the angles of incidence and refraction with the refractive indices of the two media. It states:
n1 * sin(i) = n2 * sin(r')
where n1 and n2 are the refractive indices of the first and second media, respectively.
Applying Snell's Law:
Since sin(90º) = 1, the equation becomes:
n1 * sin(60º) = n2 * 1
Simplifying the equation:
n1 * √3/2 = n2
We are given that the angle of incidence is 60º. The sine of 60º is √3/2. Substituting these values into the equation:
n1 * √3/2 = n2
Since the reflected and refracted rays are normal to each other, the refracted ray is perpendicular to the interface. This means it is traveling along the normal to the interface, which implies that the refractive index of the second medium is 1. Therefore, n2 = 1.
The equation becomes:
n1 * √3/2 = 1
Simplifying further:
n1 = 2/√3
Rationalizing the denominator:
n1 = 2√3/3
Therefore, the refractive index of the material of the plate is 2√3/3, which is approximately 1.732.
Answer:
The correct answer is option C) 1.732.
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When light falls on a given plate at angle of incidence of 60º, the reflected and refracted rays are found to be normal to each other. The refractive index of the material of the plate is thena)0.866b)1.5c)1.732d)2Correct answer is option 'C'. Can you explain this answer?
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