Question

What is the time taken in seconds to cross a glass plate of thickness $6 \mathrm{~mm}\( and \)\mu=2.0$ by light ? (A) \(8 \times 10^{-11}\) (B) \(4 \times 10^{-11}\) (C) \(2 \times 10^{11}\) (D) \(16 \times 10^{-11}\)

Short answer

The time taken by light to cross the glass plate is \(4 \times 10^{-11}\, \text{s}\).

Step-by-step solution

Convert the thickness of the glass plate into meters

We are given that the thickness of the glass plate is \(6\, \text{mm}\). We need to convert this into meters. Since 1 meter is equal to 1000 millimeters, we have : \[d = 6\, \text{mm} \times \frac{1\, \text{m}}{1000\, \text{mm}}\] \[d = 0.006\, \text{m}\]

Use the formula to calculate the time taken by light

Now, we have the distance \(d = 0.006\, \text{m}\) and the refractive index \(\mu = 2.0\). We also know that the speed of light in vacuum is \(c = 3\times 10^8 \,\text{m/s}\). We can use the formula \(t = \frac{d}{c/\mu}\) to find the time taken by light to cross the glass plate. \[t = \frac{0.006\, \text{m}}{(3 \times 10^8 \,\text{m/s}) / 2.0}\] \[t = \frac{0.006\, \text{m}}{(1.5 \times 10^8 \,\text{m/s})}\]

Calculate the time and express it in scientific notation

By performing the calculation, we can find the time taken by light in seconds: \[t = \frac{0.006\, \text{m}}{(1.5 \times 10^8\, \text{m/s})}\] \[t = 4 \times 10^{-11}\, \text{s}\] The time taken by light to cross the glass plate is \(4 \times 10^{-11}\, \text{s}\). Therefore, the correct answer is (B).