## Related questions with answers

A person working on the transmission of a car accidentally drops a bolt into a tray of oil. The oil is 5.00 cm deep. The bolt appears to be 3.40 cm beneath the surface of the oil, when viewed from directly above . What is the index of refraction of the oil?

Solutions

Verified**Concept**
The index of refraction can be described by the following equation:

$\begin{gather} n = \frac{c}{v} \end{gather}$

**Given:**

Apparent depth = $d'$ = 3.40$\text{ cm}$ Actual depth = $d$ = 5.00$\text{ cm}$

We are asked to find the refractive index of oil $n_{\text{oil}}$. We also know the refractive index of air: $n_{\text{air}} = 1$. The oil is causing the apparent depth to be different when seen from air above. So, we can write that:

$\begin{align*} d' &= d \left(\dfrac{n_{\text{air}}}{n_{\text{oil}}} \right)\\\\ 3.40\text{ cm} &= 5.00\text{ cm} \left(\dfrac{1}{n_{\text{oil}}} \right)\\\\ n_{\text{oil}} &= \dfrac{5.00\text{ cm}}{3.40\text{ cm}}\\\\ &= \boxed{1.47} \end{align*}$

So, the refractive index of oil is $1.47$.

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