Refraction of light (Refraction through one transparent medium to another)

Refraction of light

The phenomenon of a ray of light deviating from its path when it enters another transparent medium is called refraction of light.

• When a ray of light passes from a denser medium to a rarer medium, it moves away from the normal.
• When a light ray passes from a rarer medium to a denser medium, it bends towards the normal.

Law of Refraction of Light

1. The incident ray, the refracted ray and the normal at the point of incidence all lie in the same plane.
2. Snell's Law

where i ➛ angle of incidence, r ➛ angle of refraction and n₂₁ ➛ relative  refractive index (To know about click on it) 

Refraction at Spherical Surface

The rays are incident from medium 1 to medium 2 .Let Refractive index for medium 1 and medium 2 are n₁ and n₂ respectively.

The object is placed at O and image is formed at I . We take distance of object is u, distance of image is v and radius of curvature is R. Ifthe aperture (or the lateral size) of the surface to be small compared to other distances involved, so that small angle approximation can be made. The distance PQ will be taken nearly equal to the distance of perpendicular from point P on principal axis.

 Now for ∆ POC , i is the exterior angle,

                       ∴  i = ∠POQ + ∠PCQ 

 

for ∆ PIC , ∠PCQ is the exterior angle, 

                      ∴  ∠PCQ = ∠PIQ + r

                      r = ∠PCQ - ∠PIQ

Now from Snell's Law

By small angle approximation

                    n₁ i = n₂ r 

Put the values of i & r from equations (1) & (2), we get 

Here OQ = - u , PI = + v & QC = + R ( using Cartesian sign convention)