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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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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? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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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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?, a detailed solution for 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? has been provided alongside types of 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? theory, EduRev gives you an
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