The question asks for the definition of the refractive index of a medium. The refractive index is a fundamental property in optics that describes how fast light travels through a medium compared to its speed in a vacuum. It is a dimensionless quantity.
B) The speed of light in vacuum to the speed of light in that medium
This option correctly states the definition of the refractive index, which is the ratio of the speed of light in vacuum (\(c\)) to the speed of light in the given medium (\(v\)).
To find the speed of light in water, we use the definition of the refractive index. The refractive index of a medium is the ratio of the speed of light in vacuum to the speed of light in that medium.
Recall the formula for refractive index:
The refractive index (\(n\)) of a medium is given by the formula:
where:
Identify the given values:
Rearrange the formula to solve for \(v\):
\[ v = \frac{c}{n} \]Substitute the given values into the formula:
\[ v = \frac{3 \times 10^8 \text{ m/s}}{1.33} \]Calculate the speed of light in water:
\[ v \approx 2.2556 \times 10^8 \text{ m/s} \]Rounding to two decimal places, we get:
\[ v \approx 2.26 \times 10^8 \text{ m/s} \]Among the given options, \(2.25 \times 10^8 \text{ m/s}\) is the closest approximation.
Correct Option: A) The speed of light in water is approximately \(2.25 \times 10^8 \text{ m/s}\). This is derived directly from the formula \(v = c/n\), where \(c\) is the speed of light in vacuum and \(n\) is the refractive index of water.
The speed of light depends on the medium through which it travels. This speed is inversely related to the refractive index of the medium. The lower the refractive index, the faster the light travels.
Light travels fastest in a vacuum because it has the lowest refractive index (exactly 1). In a vacuum, there are no particles to interact with the light, allowing it to propagate at its maximum possible speed, which is approximately \(3 \times 10^8 \text{ m/s}\).
This question tests the understanding of refraction, specifically how light behaves when it passes from a rarer medium to a denser medium. The key concept here is Snell's Law and the change in the speed of light.
Correct Option: D) Bends towards the normal
The phenomenon of apparent depth is a direct consequence of how light behaves when it passes from one medium to another, specifically from a denser medium (water) to a rarer medium (air). We need to identify the optical principle that governs this behavior.
A) Refraction of light as it passes from water into air, bending away from the normal — This accurately describes the optical phenomenon responsible for apparent depth. When light moves from a denser medium (water) to a rarer medium (air), it refracts (bends) away from the normal, making the submerged object appear shallower.
To find the apparent depth of an object submerged in a liquid, we use the formula relating real depth, apparent depth, and the refractive index of the liquid. The observer is looking from air into the liquid.
When an observer looks from a rarer medium (air) into a denser medium (liquid), the apparent depth (\(h_{\text{apparent}}\)) is related to the real depth (\(h_{\text{real}}\)) and the refractive index (\(\mu\)) by the formula:
\[ \mu = \frac{\text{Real depth}}{\text{Apparent depth}} = \frac{h_{\text{real}}}{h_{\text{apparent}}} \]Correct Option: B) 4.5 cm