Chapter 16.1, Problem 15SSC

To determine

To Calculate: The speed of light using Roemer’s method.

To Check: Whether this method appear to be accurate or not.

To Explain: The reason why this method is accurate or not.

Answer to Problem 15SSC

The speed of light calculated by Roemer’s methods is $\boxed{c=3.01\times {10}^8{\text{ms}}^{\text{-1}}}$ and it is nearly equal to the actual value of the speed of light.

Explanation of Solution

Given:

The correct time taken for light to cross Earth orbit is $16.5\min$ .

The diameter of the Earth orbit is $2.98\times {10}^{11}\text{m}$ .

Formula used:

The expression for distance in terms of speed of light and time taken by t , can be expressed as

  $d=ct$  ...... (1)

Here, $t$ is the time taken by the light and $c$ is the speed of light.

Calculation:

Roemer’s calculated the speed of light by dividing the diameter of the earth orbit by the time taken i.e.

  $c=\frac{d}{t}$  ...... (2)

Substitute $2.98\times {10}^{11}\text{m}$ for $d$ and $16.5\min$ for $t$ in equation (2)

  $\begin{array}{l}c=\frac{2.98\times {10}^{11}\text{m}}{16.5\min }\\ c=\frac{2.98\times {10}^{11}\text{m}}{\left(16.5\times 60\right)\text{s}}\\ \boxed{c=3.01\times {10}^8{\text{ms}}^{\text{-1}}}\end{array}$

Since the value of $c$ is nearly equal to actual value which is $3.0\times {10}^8\text{m}\cdot {\text{s}}^{\text{-1}}$ .

This means that the Roemer’s method was correct and that he could have determined an accurate value of the speed of light if he had known the actual time taken for light to cross Earth’s diameter.

Conclusion:

Hence, the speed of light calculated by Roemer’s methods is $\boxed{c=3.01\times {10}^8{\text{ms}}^{\text{-1}}}$ and it is nearly equal to the actual value of the speed of light.