Step 1 : Understanding the Question:
This question deals with geometrical optics and the propagation of electromagnetic waves through different media. We are required to determine the speed of a light ray after it transitions from air into a transparent glass medium with a given refractive index.
Step 2 : Key Formulas and Approach:
The absolute refractive index \( \mu \) of a medium is defined as the ratio of the speed of light in a vacuum or air \( c \) to its speed in that specific medium \( v \).
The formula is expressed as:
\[ \mu = \frac{c}{v} \]
To find the velocity of light in the medium, we can rearrange the formula to solve for \( v \):
\[ v = \frac{c}{\mu} \]
Step 3 : Detailed Explanation:
Identify the given physical constants from the problem text: the refractive index of the glass slab is \( \mu = 1.5 \), and the speed of light in air is \( c = 3 \times 10^8 \text{ m/s} \).
Set up the rearranged formula to compute the speed of light inside the denser medium: \( v = \frac{c}{\mu} \).
Substitute the given values into this mathematical relation to obtain: \( v = \frac{3 \times 10^8 \text{ m/s}}{1.5} \).
Simplify the fraction by noting that \( 1.5 \) is equivalent to \( \frac{3}{2} \), which gives: \( v = \frac{3 \times 10^8}{\frac{3}{2}} = 2 \times 10^8 \text{ m/s} \).
This calculation confirms that the speed of light decreases when entering a medium with a higher refractive index.
Step 4 : Final Answer:
The speed of light inside the glass slab is \( 2 \times 10^8 \text{ m/s} \), which corresponds to option (A).