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Refraction at Plane and Spherical Surfaces


The speed of light in a medium depends on refractive index of the medium. \begin{align} \mu=\frac{\text{speed of light in vacuum}}{\text{speed of light in medium}}=\frac{c}{v} \end{align}

Consider two media of refractive indices $\mu_1$ and $\mu_2$ joined at the interface. An incident ray travelling in a medium of refractive index $\mu_1$ strikes at the interface. It crosses the interface and reach the other media (refracted ray). The direction of refracted ray is given by the laws of refraction:

  1. The incident ray, refracted ray and the normal (to the interface) lies in the same plane.
  2. The angle of incidence $i$, the angle of refraction $r$ and the refractive indices are related by Snell's law: \begin{align} \frac{\sin i}{\sin r}=\frac{\mu_2}{\mu_1} \end{align}


The depth of objects kept in a water containers appears to be less than their real depth. This occurs due to refraction of light. The relation between apparent depth, real depth and refractive index is \begin{align} \mu=\frac{\text{real depth}}{\text{apparent depth}}=\frac{d}{d^\prime} \end{align}



  1. Thin Lenses
  2. Total internal reflection
  3. Deviation by a Prism
JEE Physics Solved Problems in Mechanics