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A ray of light falls on a transparent glass slab of refractive index 1.62. If the reflected ray and the refracted ray are mutually perpendicular, the angle of incidence is
- a)tan-1(1.62)
- b)tan-1(1/1.62)
- c)tan-1(1.33)
- d)tan-1(1/1.33)
Correct answer is option 'A'. Can you explain this answer?
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A ray of light falls on a transparent glass slab of refractive index 1...
Explanation:
When a ray of light falls on a transparent glass slab, it undergoes reflection and refraction. The angle of incidence is the angle between the incident ray and the normal to the surface of the glass slab. The angle of reflection is the angle between the reflected ray and the normal, and the angle of refraction is the angle between the refracted ray and the normal.
In this case, the reflected ray and the refracted ray are mutually perpendicular. This means that the angle of reflection is 90 degrees. Let's assume that the angle of incidence is θ.
Using the laws of reflection and refraction:
1. Law of reflection: The angle of incidence is equal to the angle of reflection. Therefore, the angle of reflection is θ.
2. Snell's law: 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 refractive indices of the two media. In this case, the refractive index of the glass slab is 1.62. Therefore, we can write:
sin(θ)/sin(90 degrees) = 1/1.62
sin(θ) = 1/1.62
Using the trigonometric identity:
sin^2(θ) + cos^2(θ) = 1
Substituting the value of sin(θ) from Snell's law:
(1/1.62)^2 + cos^2(θ) = 1
1/2.6244 + cos^2(θ) = 1
cos^2(θ) = 1 - 1/2.6244
cos^2(θ) = 0.6177
cos(θ) = sqrt(0.6177)
cos(θ) = 0.7855
Using the trigonometric identity:
tan^2(θ) + 1 = sec^2(θ)
Substituting the value of cos(θ) from the previous step:
tan^2(θ) + 1 = 1/0.6177
tan^2(θ) = 1/0.6177 - 1
tan^2(θ) = 0.6177/0.6177 - 1
tan^2(θ) = 1 - 0.6177/0.6177
tan^2(θ) = 0.3823/0.6177
tan^2(θ) = 0.6189
tan(θ) = sqrt(0.6189)
tan(θ) = 0.7869
Therefore, the angle of incidence is:
θ = tan^(-1)(0.7869)
Hence, the correct answer is option 'A': tan^(-1)(1.62).
When a ray of light falls on a transparent glass slab, it undergoes reflection and refraction. The angle of incidence is the angle between the incident ray and the normal to the surface of the glass slab. The angle of reflection is the angle between the reflected ray and the normal, and the angle of refraction is the angle between the refracted ray and the normal.
In this case, the reflected ray and the refracted ray are mutually perpendicular. This means that the angle of reflection is 90 degrees. Let's assume that the angle of incidence is θ.
Using the laws of reflection and refraction:
1. Law of reflection: The angle of incidence is equal to the angle of reflection. Therefore, the angle of reflection is θ.
2. Snell's law: 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 refractive indices of the two media. In this case, the refractive index of the glass slab is 1.62. Therefore, we can write:
sin(θ)/sin(90 degrees) = 1/1.62
sin(θ) = 1/1.62
Using the trigonometric identity:
sin^2(θ) + cos^2(θ) = 1
Substituting the value of sin(θ) from Snell's law:
(1/1.62)^2 + cos^2(θ) = 1
1/2.6244 + cos^2(θ) = 1
cos^2(θ) = 1 - 1/2.6244
cos^2(θ) = 0.6177
cos(θ) = sqrt(0.6177)
cos(θ) = 0.7855
Using the trigonometric identity:
tan^2(θ) + 1 = sec^2(θ)
Substituting the value of cos(θ) from the previous step:
tan^2(θ) + 1 = 1/0.6177
tan^2(θ) = 1/0.6177 - 1
tan^2(θ) = 0.6177/0.6177 - 1
tan^2(θ) = 1 - 0.6177/0.6177
tan^2(θ) = 0.3823/0.6177
tan^2(θ) = 0.6189
tan(θ) = sqrt(0.6189)
tan(θ) = 0.7869
Therefore, the angle of incidence is:
θ = tan^(-1)(0.7869)
Hence, the correct answer is option 'A': tan^(-1)(1.62).
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A ray of light falls on a transparent glass slab of refractive index 1.62. If the reflected ray and the refracted ray are mutually perpendicular, the angle of incidence isa)tan-1(1.62)b)tan-1(1/1.62)c)tan-1(1.33)d)tan-1(1/1.33)Correct answer is option 'A'. Can you explain this answer?
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A ray of light falls on a transparent glass slab of refractive index 1.62. If the reflected ray and the refracted ray are mutually perpendicular, the angle of incidence isa)tan-1(1.62)b)tan-1(1/1.62)c)tan-1(1.33)d)tan-1(1/1.33)Correct answer is option 'A'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A ray of light falls on a transparent glass slab of refractive index 1.62. If the reflected ray and the refracted ray are mutually perpendicular, the angle of incidence isa)tan-1(1.62)b)tan-1(1/1.62)c)tan-1(1.33)d)tan-1(1/1.33)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ray of light falls on a transparent glass slab of refractive index 1.62. If the reflected ray and the refracted ray are mutually perpendicular, the angle of incidence isa)tan-1(1.62)b)tan-1(1/1.62)c)tan-1(1.33)d)tan-1(1/1.33)Correct answer is option 'A'. Can you explain this answer?.
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