Refraction of Light , Laws of Refraction , Relation between Real depth and Apparent depth

In a homogeneous medium light travels along a straight line. When light changes medium it deviates from its path. ” Variation of the path of the ray due to variation of the medium is called refraction.

To study the refraction we need to understand the term refractive index. We will use the alphabet n to represent the refractive index.
Absolute refractive index of a medium is equal to

n = speed of light in vacuum /speed of light in medium

Laws of Refraction :

1st Law : – Incident ray, refracted ray and normal to the interface separating the media at the point of incidence all lie in same plane.

2nd Law:- Suppose light travels from medium I to medium II and absolute refractive indices of the corresponding media are n₁ and n₂.

If θ₁ and θ₂ are the angle of incidence and angle of refraction respectively then

n₁ sin θ₁ = n₂ sin θ₂ .

This law is known as Snell’s law.

From above expression, $\displaystyle \frac{sin\theta_2}{sin\theta_1} = \frac{n_1}{n_2}$

” If n₁ > n₂, then sin θ₂ > sin θ₁, hence θ₂ > θ₁ as a result refracted ray will bend away from normal.” Converse of this statement is also true.

Refraction at plane surface:

Relation between Real and Apparent depth (for Normal Vision) :

First of all we define the term normal vision. If object and viewer both are in different media and eyes lie near the normal to the inter-face which passes through the object then vision is known as normal vision.

For the normal vision angle of incidence and corresponding angle of refraction, both are very small.

In the figure shown ‘ O ‘ is an object placed in medium II and viewer is situated in medium I from figure

$ \displaystyle sini \approx tani = \frac{AB}{OA} $ …(i)

$ \displaystyle sinr \approx tanr = \frac{AB}{O’A} $ …(ii)

$ \displaystyle \frac{sini}{sinr} = \frac{O’A}{OA} = \frac{n_1}{n_2} $

$ \displaystyle O’A = \frac{n_1}{n_2}OA $

For the sake of convenience here we replace n₁ by n_v (refractive index of the medium in which viewer is situated) and n₂ = n₀ (refractive index of the medium in which object is placed).

$ \displaystyle Apparent\, Depth = (Real \, Depth) \frac{n_v}{n_o} $

If n_v > n_o then apparent depth is more than real depth and vice-versa.

Shift = real depth − apparent depth

$ \displaystyle S = OA(1-\frac{n_v}{n_o} ) $

Also Read :

→ Reflection of Light at a Plane Surface → Reflection at Spherical Surface & Mirror Formula → Lateral Magnification → Refraction through Number of media → Total internal reflection → Refraction through a prism → Angle of minimum deviation & Prism Formula → Refraction at Curved surface → Lens maker’s formula → Combinations of Lenses → Simple Magnifier → Compound Microscope → Telescope

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