MP Board · Class 10 · Science · Light – Reflection and RefractionDefine refraction of light. State the laws of refraction. Explain absolute refractive index and relative refractive index with necessary mathematical formulas. Also, explain why a pencil partially immersed in water appears bent at the interface.

Definition of Refraction\nRefraction of light is the phenomenon of the change in the path of light when it passes obliquely from one transparent medium to another transparent medium. This change in direction occurs because the speed of light changes as it enters from one medium into another. The medium in which the speed of light is more is called an optically rarer medium, and the medium in which the speed of light is less is called an optically denser medium. When a ray of light travels from a rarer medium to a denser medium, it bends towards the normal. Conversely, when it travels from a denser medium to a rarer medium, it bends away from the normal.

Laws of Refraction\nRefraction of light obeys two fundamental laws, which are known as Snell's laws of refraction:

• First Law: The incident ray, the refracted ray, and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.
• Second Law: The ratio of the sine of the angle of incidence ($i$) to the sine of the angle of refraction ($r$) is a constant for the light of a given color and for the given pair of media. Mathematically, it is expressed as: $$\frac{\sin i}{\sin r} = \text{constant} = n_{21}$$\nThis constant value is called the refractive index of the second medium with respect to the first.

Refractive Index

• Absolute Refractive Index ($n$): When light travels from a vacuum or air into a given medium, the refractive index of that medium with respect to vacuum is called absolute refractive index. It is given by the ratio of the speed of light in vacuum ($c$) to the speed of light in the medium ($v$): $$n = \frac{c}{v}$|
• Relative Refractive Index ($n_{21}$): When light travels from medium 1 to medium 2, the relative refractive index is the ratio of the speed of light in medium 1 ($v_1$) to the speed of light in medium 2 ($v_2$): $$n_{21} = \frac{v_1}{v_2} = \frac{n_2}{n_1}$$

Reason for Bent Pencil Phenomenon\nWhen a pencil is partially immersed in water, light rays coming from the submerged part of the pencil travel from water (denser medium) to air (rarer medium). According to the laws of refraction, these rays bend away from the normal as they enter the air. When these refracted rays reach the observer's eyes, they appear to come from a point higher than their actual position. Consequently, the immersed portion of the pencil appears raised, making the pencil look bent at the air-water interface.