Question

what is the speed of light in ethyl alcohol (n = 1.36)?
express your answer to three significant figures and include the appropriate units.
v = value units
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part b
what is the speed of light in lucite (n = 1.50)?
express your answer to three significant figures and include the appropriate units.

Explanation:

Step1: Recall the formula for speed of light in a medium

The speed of light \( v \) in a medium with refractive index \( n \) is given by \( v=\frac{c}{n} \), where \( c = 3.00\times10^{8}\space m/s \) (speed of light in vacuum).

Step2: Calculate speed in ethyl alcohol (\( n = 1.36 \))

Substitute \( c = 3.00\times 10^{8}\space m/s \) and \( n=1.36 \) into the formula:
\( v=\frac{3.00\times 10^{8}}{1.36}\approx2.20588\times 10^{8}\space m/s \). Rounding to three significant figures, we get \( 2.21\times 10^{8}\space m/s \).

Step3: Calculate speed in lucite (\( n = 1.50 \))

Substitute \( c = 3.00\times 10^{8}\space m/s \) and \( n = 1.50 \) into the formula:
\( v=\frac{3.00\times 10^{8}}{1.50}=2.00\times 10^{8}\space m/s \).

Answer:

For ethyl alcohol: \( v = 2.21\times 10^{8}\space m/s \)
For lucite: \( v=2.00\times 10^{8}\space m/s \)