Question

The seven colors of incident light can be recombined when two prisms are placed in ?

Answer 1

Hint:Light bends on the interface of two media. These refractions are different for different wavelengths, and can be negated by putting an inverted prism in the path of dispersed light. Since light has different speeds in different media the light rays bend at the interface of two media, due to change in respective wavelengths.

Complete answer:
The amount by which a ray of light is bent at the interface of two media is indicated by their refractive indices w.r.t. each other;
$\mu =\dfrac{\sin i}{\sin r}$
where $i$ and $r$ are the angles of incidence and refraction respectively. White light is made of seven different colors, each corresponding to a particular wavelength. Each of these wavelengths behaves differently at the interface of two media, i.e., bend a different amount.

The relation between the amount of bending ($\mu $) and the wavelength ‘$\lambda $’ is given by Euler’s equation which is:
$\mu =A+\dfrac{B}{{{\lambda }^{2}}}+\dfrac{C}{{{\lambda }^{4}}}.....$
Hence from the above equation we have that the color of light corresponds to a higher wavelength of light (ex. Red) has a higher refractive index, therefore bending by a greater amount than a color corresponding to lower wavelengths of light(ex. Violet). This phenomenon results in the dispersion of light.

Now after the light has been dispersed by the first prism, the effects of dispersion by the first prism can be negated if we make the dispersed light pass through an exactly same prism of the same angle but in the inverted direction. This allows each color of light to bend exactly by the same amount as in the first refraction but in the opposite direction; thereby negating the dispersion effects and hence returning white light out of the setup.

Note:A rectangular prism bends a light ray to an extent which is controlled by its refractive index which in turn depends on the wavelength of light. Inverting the same prism in the path of the dispersed light just negates the effects of dispersion of the original prism.