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A ray of light strikes a glass plate at an angle θ. If angle between the reflected and refracted rays is a right angle, then refractive index of the glass plate is given by
- a)μ=sin θ
- b)μ=cos θ
- c)μ=tan θ
- d)μ=cot θ
Correct answer is option 'C'. Can you explain this answer?
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A ray of light strikes a glass plate at an angle θ. If angle between t...
Explanation:
- When light passes through a medium of higher refractive index, it bends towards the normal and when it passes through a medium of lower refractive index, it bends away from the normal.
- When a ray of light strikes a glass plate at an angle θ, it is partly reflected and partly refracted.
- Let the angle of incidence be i, the angle of reflection be r and the angle of refraction be t. Then, we have:
i + r = 90° (angle of incidence + angle of reflection = 90°)
t + r = 90° (angle of refraction + angle of reflection = 90°)
- Using Snell's law, we can relate the angles of incidence and refraction to the refractive index of the glass plate. Snell's law is given by:
n1 sin i = n2 sin r
where n1 is the refractive index of the medium from which the light is coming (in this case, air), n2 is the refractive index of the glass plate and i and r are the angles of incidence and refraction respectively.
- From the first equation above, we have r = 90° - i. Substituting this in the second equation, we get:
t + (90° - i) = 90°
t = i
- Therefore, the angle of refraction is equal to the angle of incidence.
- Using Snell's law, we can now write:
n1 sin i = n2 sin i
- Dividing both sides by sin i, we get:
n2 = n1 / sin i
- Therefore, the refractive index of the glass plate is given by:
μ = n2 = n1 / sin i
- Substituting the value of i from the first equation above, we get:
μ = n1 / sin(90° - r) = n1 / cos r
- Using the trigonometric identity cos r = sin(90° - r), we can simplify this to:
μ = n1 sin r / cos r = tan r
- But we know that r + t = 90°, so we can write:
tan r = tan(90° - t) = cot t
- Therefore, the refractive index of the glass plate is given by:
μ = cot t = cot i
- Option C is the correct answer.
- When light passes through a medium of higher refractive index, it bends towards the normal and when it passes through a medium of lower refractive index, it bends away from the normal.
- When a ray of light strikes a glass plate at an angle θ, it is partly reflected and partly refracted.
- Let the angle of incidence be i, the angle of reflection be r and the angle of refraction be t. Then, we have:
i + r = 90° (angle of incidence + angle of reflection = 90°)
t + r = 90° (angle of refraction + angle of reflection = 90°)
- Using Snell's law, we can relate the angles of incidence and refraction to the refractive index of the glass plate. Snell's law is given by:
n1 sin i = n2 sin r
where n1 is the refractive index of the medium from which the light is coming (in this case, air), n2 is the refractive index of the glass plate and i and r are the angles of incidence and refraction respectively.
- From the first equation above, we have r = 90° - i. Substituting this in the second equation, we get:
t + (90° - i) = 90°
t = i
- Therefore, the angle of refraction is equal to the angle of incidence.
- Using Snell's law, we can now write:
n1 sin i = n2 sin i
- Dividing both sides by sin i, we get:
n2 = n1 / sin i
- Therefore, the refractive index of the glass plate is given by:
μ = n2 = n1 / sin i
- Substituting the value of i from the first equation above, we get:
μ = n1 / sin(90° - r) = n1 / cos r
- Using the trigonometric identity cos r = sin(90° - r), we can simplify this to:
μ = n1 sin r / cos r = tan r
- But we know that r + t = 90°, so we can write:
tan r = tan(90° - t) = cot t
- Therefore, the refractive index of the glass plate is given by:
μ = cot t = cot i
- Option C is the correct answer.
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A ray of light strikes a glass plate at an angle θ. If angle between the reflected and refracted rays is a right angle, then refractive index of the glass plate is given bya) μ=sin θ b) μ=cos θ c) μ=tan θ d) μ=cot θ Correct answer is option 'C'. Can you explain this answer?
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