Question

Light travels through a glass plate of thickness \(d\) and refractive index \(\mu\). If \(c\) is the velocity of light in vacuum, the time taken by the light to travel the thickness of glass \(d\) is

• A. \( \dfrac{d}{\mu c} \)
• B. \( \dfrac{dc}{\mu} \)
• C. \( d\mu c \)
• D. \( \dfrac{\mu d}{c} \)

Hint:

Always express speed in the medium first using \( v = \dfrac{c}{\mu} \).

Answer 1

The Correct Option is D

Step 1: Definition of refractive index.
Refractive index is defined as:
\[ \mu = \frac{c}{v} \] where \(v\) is velocity of light in glass.
Step 2: Velocity of light in glass.
\[ v = \frac{c}{\mu} \]
Step 3: Time taken to travel thickness \(d\).
\[ t = \frac{\text{distance}}{\text{velocity}} = \frac{d}{v} \]
Step 4: Substituting value of \(v\).
\[ t = \frac{d}{c/\mu} = \frac{\mu d}{c} \]
Step 5: Conclusion.
The time taken by light to pass through the glass plate is \(\dfrac{\mu d}{c}\).