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During determination of refractive index of water by means of a travelling microscope, the focus of the microscope on the bottom mark with the empty beaker has reading x. Reading of microscope is y. When the same mark is focussed on the water filled beaker, the distance between water surface and microscope is l measured by a scale. All readings suffer an error of 1%. The percentage error in the determination of refractive index is n%. Find the value of n. I need it urgently?
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Problem Analysis:
In this problem, we need to determine the refractive index of water using a travelling microscope. The focus of the microscope on the bottom mark with an empty beaker is given as reading x, and the reading of the microscope is given as y. When the same mark is focused on the water-filled beaker, the distance between the water surface and the microscope is measured as l using a scale. It is mentioned that all readings suffer an error of 1%. We need to find the percentage error in the determination of the refractive index.
Solution:
Let's assume the refractive index of water as 'n' and the actual distance between the microscope and the bottom mark in the empty beaker as 'd'.
The distance between the microscope and the bottom mark in the empty beaker, as measured by the microscope, is given as x. Since there's a 1% error in the reading, the actual distance can be calculated as:
Actual distance (d) = x - (1% of x) = x - (0.01x) = 0.99x
Similarly, the distance between the microscope and the bottom mark in the water-filled beaker, as measured by the scale, is given as l. Since there's a 1% error in the reading, the actual distance can be calculated as:
Actual distance (d) = l + (1% of l) = l + (0.01l) = 1.01l
The apparent shift in the position of the bottom mark due to the refraction of light can be given by the formula:
Apparent shift = (n - 1) * d
The apparent shift can also be calculated as the difference between the actual distances measured in the empty beaker and water-filled beaker:
Apparent shift = 0.99x - 1.01l
Equating the two expressions for apparent shift, we get:
0.99x - 1.01l = (n - 1) * d
Since we need to find the percentage error in the determination of the refractive index, we can calculate the relative error by taking the ratio of the absolute error to the actual value:
Relative error in refractive index = (|n - actual value| / actual value) * 100
Substituting the value of apparent shift, we get:
Relative error in refractive index = (|(0.99x - 1.01l) - (n - 1) * d| / (n - 1) * d) * 100
Simplifying the expression, we get:
Relative error in refractive index = (|0.99x - 1.01l - (n - 1) * (0.99x - 1.01l)| / (n - 1) * (0.99x - 1.01l)) * 100
Since the error in all readings is 1%, the values of x, l, and d can also be expressed as:
Actual value of x = x - (0.01x) = 0.99x
Actual value of l = l + (0.01l) = 1.01l
Actual value of d = 0.99x
Substituting these values in the expression for relative error, we get:
Relative
In this problem, we need to determine the refractive index of water using a travelling microscope. The focus of the microscope on the bottom mark with an empty beaker is given as reading x, and the reading of the microscope is given as y. When the same mark is focused on the water-filled beaker, the distance between the water surface and the microscope is measured as l using a scale. It is mentioned that all readings suffer an error of 1%. We need to find the percentage error in the determination of the refractive index.
Solution:
Let's assume the refractive index of water as 'n' and the actual distance between the microscope and the bottom mark in the empty beaker as 'd'.
The distance between the microscope and the bottom mark in the empty beaker, as measured by the microscope, is given as x. Since there's a 1% error in the reading, the actual distance can be calculated as:
Actual distance (d) = x - (1% of x) = x - (0.01x) = 0.99x
Similarly, the distance between the microscope and the bottom mark in the water-filled beaker, as measured by the scale, is given as l. Since there's a 1% error in the reading, the actual distance can be calculated as:
Actual distance (d) = l + (1% of l) = l + (0.01l) = 1.01l
The apparent shift in the position of the bottom mark due to the refraction of light can be given by the formula:
Apparent shift = (n - 1) * d
The apparent shift can also be calculated as the difference between the actual distances measured in the empty beaker and water-filled beaker:
Apparent shift = 0.99x - 1.01l
Equating the two expressions for apparent shift, we get:
0.99x - 1.01l = (n - 1) * d
Since we need to find the percentage error in the determination of the refractive index, we can calculate the relative error by taking the ratio of the absolute error to the actual value:
Relative error in refractive index = (|n - actual value| / actual value) * 100
Substituting the value of apparent shift, we get:
Relative error in refractive index = (|(0.99x - 1.01l) - (n - 1) * d| / (n - 1) * d) * 100
Simplifying the expression, we get:
Relative error in refractive index = (|0.99x - 1.01l - (n - 1) * (0.99x - 1.01l)| / (n - 1) * (0.99x - 1.01l)) * 100
Since the error in all readings is 1%, the values of x, l, and d can also be expressed as:
Actual value of x = x - (0.01x) = 0.99x
Actual value of l = l + (0.01l) = 1.01l
Actual value of d = 0.99x
Substituting these values in the expression for relative error, we get:
Relative
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During determination of refractive index of water by means of a travelling microscope, the focus of the microscope on the bottom mark with the empty beaker has reading x. Reading of microscope is y. When the same mark is focussed on the water filled beaker, the distance between water surface and microscope is l measured by a scale. All readings suffer an error of 1%. The percentage error in the determination of refractive index is n%. Find the value of n. I need it urgently?
Question Description
During determination of refractive index of water by means of a travelling microscope, the focus of the microscope on the bottom mark with the empty beaker has reading x. Reading of microscope is y. When the same mark is focussed on the water filled beaker, the distance between water surface and microscope is l measured by a scale. All readings suffer an error of 1%. The percentage error in the determination of refractive index is n%. Find the value of n. I need it urgently? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about During determination of refractive index of water by means of a travelling microscope, the focus of the microscope on the bottom mark with the empty beaker has reading x. Reading of microscope is y. When the same mark is focussed on the water filled beaker, the distance between water surface and microscope is l measured by a scale. All readings suffer an error of 1%. The percentage error in the determination of refractive index is n%. Find the value of n. I need it urgently? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for During determination of refractive index of water by means of a travelling microscope, the focus of the microscope on the bottom mark with the empty beaker has reading x. Reading of microscope is y. When the same mark is focussed on the water filled beaker, the distance between water surface and microscope is l measured by a scale. All readings suffer an error of 1%. The percentage error in the determination of refractive index is n%. Find the value of n. I need it urgently?.
During determination of refractive index of water by means of a travelling microscope, the focus of the microscope on the bottom mark with the empty beaker has reading x. Reading of microscope is y. When the same mark is focussed on the water filled beaker, the distance between water surface and microscope is l measured by a scale. All readings suffer an error of 1%. The percentage error in the determination of refractive index is n%. Find the value of n. I need it urgently? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about During determination of refractive index of water by means of a travelling microscope, the focus of the microscope on the bottom mark with the empty beaker has reading x. Reading of microscope is y. When the same mark is focussed on the water filled beaker, the distance between water surface and microscope is l measured by a scale. All readings suffer an error of 1%. The percentage error in the determination of refractive index is n%. Find the value of n. I need it urgently? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for During determination of refractive index of water by means of a travelling microscope, the focus of the microscope on the bottom mark with the empty beaker has reading x. Reading of microscope is y. When the same mark is focussed on the water filled beaker, the distance between water surface and microscope is l measured by a scale. All readings suffer an error of 1%. The percentage error in the determination of refractive index is n%. Find the value of n. I need it urgently?.
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