Question

What is the speed of light in crown glass with refractive index 1.52?

Answer 1

Hint: In order to solve the question, we will take out the speed of light in air so as to substitute it in the relation of refractive index , speed of light in air and speed of light in medium after then we will calculate the speed of light in crown glass by substituting refractive of index of crown glass and hence we will reach to our answer

Formula Used:
${\text{Refractive index = }}\dfrac{{{\text{Speed of light in air}}}}{{{\text{Speed of light in medium}}}}$

Complete step by step answer:
In the question we are given the refractive index of the crown glass and we have to find the speed of light in the crown
Refractive index of crown glass = 1.52
In order to find the speed of light in the crown glass we will use the formula
${\text{Refractive index = }}\dfrac{{{\text{Speed of light in air}}}}{{{\text{Speed of light in medium}}}}$
Here in this question medium is crown glass hence the formula will be altered and becomes
${\text{Refractive index of crown glass = }}\dfrac{{{\text{speed of light in air}}}}{{{\text{Speed of light in crown glass}}}}$
Now we will substitute the value of refractive index of crown glass as given in the question we will substitute the value of speed of light in air that is
Speed of light in air = $3 \times {10^8}m{s^{ - 1}}$
Therefore, after substituting we get
${\text{1}}{\text{.52 = }}\dfrac{{3 \times {{10}^8}m{s^{ - 1}}}}{{{\text{Speed of light in crown glass}}}}$
Now we will take speed of light in crown glass on the numerator of left-hand side and we take refractive index of crown of glass on denominator of right-hand side
${\text{Speed of light in crown glass = }}\dfrac{{3 \times {{10}^8}m{s^{ - 1}}}}{{1.52}}$
Therefore, the speed of light in crown glass comes out to be
${\text{Speed of light in crown glass = 1}}{\text{.97}} \times {10^8}m{s^{ - 1}}$
Hence, the answer is ${\text{1}}{\text{.97}} \times {10^8}m{s^{ - 1}}$.

Note: Many of the people will may wonder that why the refractive index doesn’t have any standard international unit or SI unit this is because it the division of the speed of light in air and speed of light in another medium so as both of them are speeds their units will be cut out and makes refractive index unitless