Question

Light travels with a speed of \(2\times 10^{8}\,m/s\) in crown glass of refractive index 1.5. What is the speed of light in 1.8?

• A. \(1.33\times 10^{8}\,m/s\)
• B. \(1.67\times 10^{8}\,m/s\)
• C. \(2.0\times 10^{8}\,m/s\)
• D. \(3.0\times 10^{8}\,m/s\)

Hint:

Speed in medium: \(v=\frac{c}{n}\). Higher refractive index means lower speed.

Answer 1

The Correct Option is B

Step 1: Use refractive index relation.
\[ n = \frac{c}{v} \Rightarrow c = nv \]
Step 2: Find speed of light in vacuum using glass data.
Given:
\[ n_1 = 1.5,\quad v_1 = 2\times 10^{8}\,m/s \]
So:
\[ c = n_1 v_1 = 1.5 \times 2\times 10^{8} = 3\times 10^{8}\,m/s \]
Step 3: Find speed in medium with refractive index 1.8.
\[ v_2 = \frac{c}{n_2} = \frac{3\times 10^{8}}{1.8} = 1.67\times 10^{8}\,m/s \]
Final Answer:
\[ \boxed{1.67\times 10^{8}\,m/s} \]