A ray of light strikes a glass plate at an angle of 60°. If the reflected and refracted rays are perpendicular to each other, then refractive index of glass isa)3/2b)√3c)√3/2d)1/2Correct answer is option 'B'. Can you explain this answer?

Question

A ray of light strikes a glass plate at an angle of 60&#176;. If the reflected and refracted rays are perpendicular to each other, then refractive index of glass is&#8203;a)3/2b)&#8730;3c)&#8730;3/2d)1/2Correct answer is option 'B'. Can you explain this answer?

Answer

Given from figure angle of incidence i=600
angle of refraction r=30⁰
We know μ= sin i/sin r
μ= sin60/sin30 =((√3)/2) ×2=√3

Answer

Mu(refractive index) =sin theta/cos theta.Mu=sin60/cos60.Mu=√3/2/1/2.Mu=√3.....

Answer

Given:
- Angle of incidence (i) = 60°
- Reflected and refracted rays are perpendicular to each other.

To find: Refractive index of glass

Explanation:
When a ray of light passes from one medium to another, it undergoes reflection and refraction. The angle of incidence, angle of reflection, angle of refraction, and refractive index of the mediums are related by Snell's law.

Snell's Law:
Snell's law 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 media.

Mathematically, it can be written as:
sin(i)/sin(r) = v1/v2

Where:
- i is the angle of incidence
- r is the angle of refraction
- v1 is the speed of light in the first medium
- v2 is the speed of light in the second medium

Reflected Ray:
According to the given information, the reflected ray is perpendicular to the refracted ray. This means that the angle of reflection is 90°. The angle of incidence and the angle of reflection are always equal, so the angle of incidence is also 90°.

Therefore, the angle of incidence (i) = 60° = 90°

Refracted Ray:
Since the angle of incidence is 90°, the angle of refraction can be calculated using Snell's law.

sin(i)/sin(r) = v1/v2

sin(90°)/sin(r) = v1/v2

1/sin(r) = v1/v2

sin(r) = v2/v1

The sine of the angle of refraction is equal to the ratio of the speeds of light in the two media.

Perpendicularity Condition:
The refractive index (n) of a medium is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the medium (v).

n = c/v

If the reflected and refracted rays are perpendicular to each other, then the refractive index of the medium can be expressed as:

n = sin(r)/sin(i) = v2/v1

Substituting the given values:
sin(r) = v2/v1 = 1 (since the refracted ray is perpendicular to the reflected ray)

Therefore, the refractive index of glass is 1.

Conclusion:
The correct option is (d) 1/2.

Answer

Given from figure angle of incidence i=600
angle of refraction r=30⁰
We know μ= sin i/sin r
μ= sin60/sin30 =((√3)/2) ×2=√3

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