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A ray of light travelling from air enters a liquid at an angle of 45 degree with the normal . If the corresponding angle of refraction is 30 degree, then the refractive index of the liquid with respect to air is . A)1.44 B)1.41 C)1.21 D)1.45?
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A ray of light travelling from air enters a liquid at an angle of 45 d...
**Given Data:**
- Angle of incidence (i) = 45°
- Angle of refraction (r) = 30°
**To Find:**
Refractive index of the liquid with respect to air.
**Formula:**
The refractive index (n) can be calculated using Snell's law:
n = sin(i) / sin(r)
**Solution:**
1. First, we need to convert the angles from degrees to radians since the trigonometric functions in the formula use radians. We can use the following conversions:
- Angle in radians = Angle in degrees * π / 180
- Angle in degrees = Angle in radians * 180 / π
Therefore, converting the given angles to radians:
- Angle of incidence (i) = 45° * π / 180 = π / 4 radians
- Angle of refraction (r) = 30° * π / 180 = π / 6 radians
2. Now, substitute the values into Snell's law formula:
n = sin(i) / sin(r)
n = sin(π / 4) / sin(π / 6)
3. Use the trigonometric identities to simplify the equation:
n = (1 / √2) / (1 / 2)
n = 2 / √2
n = √2
4. Rationalize the denominator by multiplying both the numerator and the denominator by √2:
n = (√2 * 2) / (√2 * √2)
n = 2√2 / 2
n = √2
5. The final answer is the square root of 2, which is approximately 1.414.
**Answer:**
Therefore, the refractive index of the liquid with respect to air is approximately 1.414.
Option B) 1.41 is the correct answer.
- Angle of incidence (i) = 45°
- Angle of refraction (r) = 30°
**To Find:**
Refractive index of the liquid with respect to air.
**Formula:**
The refractive index (n) can be calculated using Snell's law:
n = sin(i) / sin(r)
**Solution:**
1. First, we need to convert the angles from degrees to radians since the trigonometric functions in the formula use radians. We can use the following conversions:
- Angle in radians = Angle in degrees * π / 180
- Angle in degrees = Angle in radians * 180 / π
Therefore, converting the given angles to radians:
- Angle of incidence (i) = 45° * π / 180 = π / 4 radians
- Angle of refraction (r) = 30° * π / 180 = π / 6 radians
2. Now, substitute the values into Snell's law formula:
n = sin(i) / sin(r)
n = sin(π / 4) / sin(π / 6)
3. Use the trigonometric identities to simplify the equation:
n = (1 / √2) / (1 / 2)
n = 2 / √2
n = √2
4. Rationalize the denominator by multiplying both the numerator and the denominator by √2:
n = (√2 * 2) / (√2 * √2)
n = 2√2 / 2
n = √2
5. The final answer is the square root of 2, which is approximately 1.414.
**Answer:**
Therefore, the refractive index of the liquid with respect to air is approximately 1.414.
Option B) 1.41 is the correct answer.
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A ray of light travelling from air enters a liquid at an angle of 45 degree with the normal . If the corresponding angle of refraction is 30 degree, then the refractive index of the liquid with respect to air is . A)1.44 B)1.41 C)1.21 D)1.45?
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A ray of light travelling from air enters a liquid at an angle of 45 degree with the normal . If the corresponding angle of refraction is 30 degree, then the refractive index of the liquid with respect to air is . A)1.44 B)1.41 C)1.21 D)1.45? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A ray of light travelling from air enters a liquid at an angle of 45 degree with the normal . If the corresponding angle of refraction is 30 degree, then the refractive index of the liquid with respect to air is . A)1.44 B)1.41 C)1.21 D)1.45? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ray of light travelling from air enters a liquid at an angle of 45 degree with the normal . If the corresponding angle of refraction is 30 degree, then the refractive index of the liquid with respect to air is . A)1.44 B)1.41 C)1.21 D)1.45?.
A ray of light travelling from air enters a liquid at an angle of 45 degree with the normal . If the corresponding angle of refraction is 30 degree, then the refractive index of the liquid with respect to air is . A)1.44 B)1.41 C)1.21 D)1.45? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about A ray of light travelling from air enters a liquid at an angle of 45 degree with the normal . If the corresponding angle of refraction is 30 degree, then the refractive index of the liquid with respect to air is . A)1.44 B)1.41 C)1.21 D)1.45? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A ray of light travelling from air enters a liquid at an angle of 45 degree with the normal . If the corresponding angle of refraction is 30 degree, then the refractive index of the liquid with respect to air is . A)1.44 B)1.41 C)1.21 D)1.45?.
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