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A student when discussing the properties of a medium(except vacuum)writesVelocity of light in vacuum = velocity of light in mediumThis formula is
- a)Dimensionally correct
- b)Dimensionally incorrect
- c)Numerically incorrect
- d)Both a anc c
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A student when discussing the properties of a medium(except vacuum)wri...
Because both are velocities, so both have same dimensions, but since velocity depends upon the medium, so both will have different numerical values. therefore, the above statement is dimensionally correct but numerically incorrect.
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A student when discussing the properties of a medium(except vacuum)wri...
Explanation:
When discussing the properties of a medium (except vacuum), the velocity of light can be expressed as:
Velocity of light in vacuum = Velocity of light in medium
Let's analyze each option to determine if the formula is dimensionally correct, numerically incorrect, or both.
a) Dimensionally correct:
To check the dimensional correctness of the formula, we need to analyze the dimensions of both sides of the equation. The dimensions of velocity are given by length/time. Therefore, the dimensions of both sides of the equation would be:
L/T = L/T
Since the dimensions on both sides are the same, the formula is dimensionally correct.
b) Dimensionally incorrect:
As discussed above, the formula is dimensionally correct. Therefore, it is not dimensionally incorrect.
c) Numerically incorrect:
To determine if the formula is numerically incorrect, we need to compare the values of the velocities in vacuum and in the medium. The velocity of light in vacuum is a fundamental constant and is denoted by "c" (approximately 3 x 10^8 m/s). On the other hand, the velocity of light in a medium is generally less than the velocity of light in vacuum. It depends on the refractive index of the medium.
Since the two velocities are generally not equal, the formula is numerically incorrect.
d) Both a and c:
After analyzing options a, b, and c, we can conclude that the formula is dimensionally correct (option a) but numerically incorrect (option c). Therefore, the correct answer is option d - both a and c.
Summary:
In summary, the formula "Velocity of light in vacuum = Velocity of light in medium" is dimensionally correct but numerically incorrect. The dimensionality of both sides of the equation is the same, but the velocities in vacuum and in the medium are generally different.
When discussing the properties of a medium (except vacuum), the velocity of light can be expressed as:
Velocity of light in vacuum = Velocity of light in medium
Let's analyze each option to determine if the formula is dimensionally correct, numerically incorrect, or both.
a) Dimensionally correct:
To check the dimensional correctness of the formula, we need to analyze the dimensions of both sides of the equation. The dimensions of velocity are given by length/time. Therefore, the dimensions of both sides of the equation would be:
L/T = L/T
Since the dimensions on both sides are the same, the formula is dimensionally correct.
b) Dimensionally incorrect:
As discussed above, the formula is dimensionally correct. Therefore, it is not dimensionally incorrect.
c) Numerically incorrect:
To determine if the formula is numerically incorrect, we need to compare the values of the velocities in vacuum and in the medium. The velocity of light in vacuum is a fundamental constant and is denoted by "c" (approximately 3 x 10^8 m/s). On the other hand, the velocity of light in a medium is generally less than the velocity of light in vacuum. It depends on the refractive index of the medium.
Since the two velocities are generally not equal, the formula is numerically incorrect.
d) Both a and c:
After analyzing options a, b, and c, we can conclude that the formula is dimensionally correct (option a) but numerically incorrect (option c). Therefore, the correct answer is option d - both a and c.
Summary:
In summary, the formula "Velocity of light in vacuum = Velocity of light in medium" is dimensionally correct but numerically incorrect. The dimensionality of both sides of the equation is the same, but the velocities in vacuum and in the medium are generally different.
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A student when discussing the properties of a medium(except vacuum)writesVelocity of light in vacuum = velocity of light in mediumThis formula isa)Dimensionally correctb)Dimensionally incorrectc)Numerically incorrectd)Both a anc cCorrect answer is option 'D'. Can you explain this answer?
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