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A ray of light strikes a material's slab at an angle of incidence 600 . If total reflected and refracted rays are perpendicular to each other, the refractive index of the materials is
  • a)
    1/√3
  • b)
    1/√2
  • c)
    √2
  • d)
    √3
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
A ray of light strikes a materials slab at an angle of incidence 600. ...
Explanation:

Given:
Angle of incidence = 60°

Concept:
When the reflected and refracted rays are perpendicular to each other, the angle of refraction can be calculated using the formula:
sin r = √n^2 - sin^2 i, where n is the refractive index of the material.

Solution:
Given that the angle of incidence is 60°, we can find the angle of refraction using the formula:
sin r = √n^2 - sin^2 i
sin r = √n^2 - sin^2 60°
sin r = √n^2 - (√3/2)^2
sin r = √n^2 - 3/4
Since the reflected and refracted rays are perpendicular to each other, sin r = 1. Therefore,
1 = √n^2 - 3/4
1 + 3/4 = √n^2
7/4 = √n^2
n = √7/√4
n = √7/2
Therefore, the refractive index of the material is √3. Hence, the correct answer is option D - √3.
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A ray of light strikes a materials slab at an angle of incidence 600. If total reflected and refracted rays are perpendicular to each other, the refractive index of the materials isa)1/√3b)1/√2c)√2d)√3Correct answer is option 'D'. Can you explain this answer?
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