Question

The dispersive power, if the refractive indices for the material of the prism are ${{\mu }_{v}}=1.6$ and $\mu_{r}=1.4,$ is:
(A) 3
(B) 1.6
(C) 0.4
(D) 1

Answer 1

HintWe know that dispersion, in wave motion, any phenomenon associated with the propagation of individual waves at speeds that depend on their wavelengths. Dispersion is sometimes called the separation of light into colours, an effect more properly called angular dispersion. Dispersion of light occurs when white light is separated into its different constituent colours because of refraction and Snell's law. White light enters a prism on the left, then is separated according to wavelength into a rainbow pattern. White light is nothing but colourless daylight. This contains all the wavelengths of the visible spectrum at equal intensity. In simple terms, electromagnetic radiation of all the frequencies in the visible range of the spectrum, appearing white to the eye, is called white light.

Complete step by step answer
We know that dispersion is a statistical term that describes the size of the distribution of values expected for a particular variable. Dispersion can be measured by several different statistics, such as range, variance, and standard deviation. Dispersion is defined as the breaking up or scattering of something. An example of a dispersion is throwing little pieces of paper all over a floor. An example of a dispersion is the coloured rays of light coming from a prism which has been hung in a sunny window.
We can add that these colours are often observed as light passes through a triangular prism. Upon passage through the prism, the white light is separated into its component colours - red, orange, yellow, green, blue and violet. The separation of visible light into its different colours is known as dispersion.
We know that it is given that:
${{\mu }_{v}}=1.6$ and $\mu_{r}=1.4,$
Now the dispersive power calculated is
by $w=\dfrac{(\mu r-\mu v)}{(u r+u v-1)}$
$w=\dfrac{(1\cdot 4-1\cdot 6)}{(1\cdot 4+1\cdot 6-1)}=0.4$

So, the correct answer is option C.

Note: We know that Snell’s Law is especially important for optical devices, such as fibre optics. Snell's Law states that the ratio of the sine of the angles of incidence and transmission is equal to the ratio of the refractive index of the materials at the interface. Snell's Law can be applied to all materials, in all phases of matter. Snell's Law is especially important for optical devices, such as fibre optics. Snell's Law states that the ratio of the sine of the angles of incidence and transmission is equal to the ratio of the refractive index of the materials at the interface. Snell's law (also known as Snell–Descartes law and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through a boundary between two different isotropic media, such as water, glass, or air.