Which of the following is a dimensionless quantity?
Correct answer: C. Refractive Index
- A. Power
- B. Frequency
- C. Refractive Index
- D. Impulse
Explanation
Refractive index of a medium is the ratio of the speed of light in a vacuum to the speed of light in that particular medium. Since the speed of light in vacuum and the speed of light in different mediums have the same dimensions, a quantity which is the ratio of these two will be dimensionless. Therefore, option C is the correct answer.For power, the formula is Energy/time and its dimensions are ML2T-3 .For frequency, the formula is 1/time period and its dimension is T-1.For impulse, the formula is force x time and its dimensions are MLT-1 . So amongst all four, only refractive index is the one having no dimensions.
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Physical quantities are expressed with SI base and derived units, while measurement limits are described through accuracy, precision, absolute and percentage error, and significant figures. Dimensional analysis checks equations, derives relationships and detects inconsistent units, but it cannot determine numerical constants or distinguish quantities with identical dimensions.
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