Question

The refractive index of water with respect to air is $1.33$. The refractive index of air with respect to water will be
$\begin{aligned} & A)0.25 \\\ & B)0.50 \\\ & C)1.00 \\\ & D)0.75 \\\ \end{aligned}$

Answer 1

The refractive index of any medium is the measurement of how much a refraction of light will pass through that medium. Multiplication of the refractive index of one medium with respect to the second medium and the refractive index of the second medium with respect to the first medium is unity.
Formula used:
${{\eta }_{12}}\times {{\eta }_{21}}=1$

Complete answer:
The physics of Ray optics contains properties of light and instrumentation of optical equipment. One of the properties of light is its refractive index. Here consider the relative refractive index of water with respect to air and vice versa.

In question given that,
Refractive index of water with respect to air is ${{\eta }_{wa}}$ .
Refractive index of air with respect to water is ${{\eta }_{aw}}$ .
And ${{\eta }_{aw}}=1.33$ .
Applying formula;

& {{\eta }_{wa}}\times {{\eta }_{aw}}=1 \\\ & \Rightarrow 1.33\times {{\eta }_{aw}}=1 \\\ & \Rightarrow {{\eta }_{aw}}=\dfrac{1}{1.33} \\\ & \Rightarrow {{\eta }_{aw}}=0.75 \\\ \end{aligned}$$ **So, the correct answer is “Option D”.** **Additional Information:** When light enters one medium to another medium the direction of light changes its direction at the surface of separating both surfaces. This phenomenon is called the refraction of light. There are two laws of refraction of light; (1)The incident ray, the refracted ray and the normal drawn at the meeting point of both the rays (the incident ray and the refracted ray) are in the same plane. (2) The ratio of the sine of the angle of the incident ray and the sine of angle of the refracted ray is constant which is called by the refractive index. Which is also called the ratio of the speed of light in the one medium and speed of light in the second medium. **Note:** There are two types of refractive index, (1) Absolute refractive index: the ratio of the speed of light in a medium and the speed of light in a vacuum is called the absolute refractive index. (2) Relative refractive index: the ratio of the speed of light in one medium and the speed of light in another medium is called a relative refractive index. If two medium is given then the symbol refractive index denoted by (Read by the refractive index of the first medium with respect to the second medium) and normally given that refractive index of a medium is the absolute refractive index.