Question

the refractive indices of the material of the prism for red and yellow colour are 1.620 and 1.635 respectively. calculate the angular dispersion and dispersive power, if refracting angle is 8 degree.

Answer 1

And i  given is detail check photo we have to find refractive index of violet first

Answer 2

Given that,

The refractive indices of the material of the prism for red colour, $n_r=1.62$

The refractive indices of the material of the prism for yellow colour, $n_y=1.635$

To find,

The angular dispersion and dispersive power.

Solution,

The formula to find the deviation of light is given by :

$\delta =(\mu-1)A$

For red light,

$\delta_r =(\mu_r-1)A$

For yellow light,

$\delta_y =(\mu_y-1)A$

For angular dispersion,

$\delta_y-\delta_r=(n_y-n_r)A\\\\\delta_y-\delta_r=(1.635 -1.620 )\times 8\\\\\delta_y-\delta_r=0.12^{\circ}$

For dispersive power,

$\omega=\dfrac{\delta_y-\delta_r}{\delta}$

Here,

$\delta=\dfrac{n_y+n_r}{2}\\\\\delta=\dfrac{1.635 +1.620 }{2}\\\\\delta=1.627$

So, dispersive power is,

$\omega=\dfrac{0.12}{1.627}\\\\\omega=0.073$

Hence, the angular dispersion and dispersive power is 0.12 degrees and 0.073 respectively.

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Angular dispersion and dispersive power

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