Question

A thin prism of crown glass (μr = 1.515, μv = 1.525) and a thin prism of flint glass (μr = 1.612, μv = 1.632) are placed in contact with each other. Their refracting angles are 5.0° each and are similarly directed. Calculate the angular dispersion produced by the combination.

Answer 1

The angular produced by the combination is 0.15°.

Explanation:

Step 1 :

In case of  crown glass  

Red colour Refractive index, $\mu_{\mathrm{cr}}$ = 1.515

Violet colour Refractive index, $\mu_{\mathrm{CV}}$ = 1.525

In case of  flint glass :

Red colour Refractive index,  $\mu_{\mathrm{fr}}$ = 1.612

Violet colour Refractive index  , $\mu_{\mathrm{fv}}$ = 1.632

Angle of Refracting ,  A = 5°

Step 2 :

Let,

$\delta_{\mathrm{c}}$ = crown glass - Angle of deviation  

$\delta_{\mathrm{f}}$  = flint glass - Angle of deviation  

Since prisms are similarly guided and put in contact with each other, the total deviation has arisen  :

$\delta=\delta_{\mathrm{c}}+\delta_{\mathrm{f}}$

  $={(\mu c}-1) A+({\mu f}-1) A$

  $=(\mu \mathrm{c}+\mu \mathrm{f}-2) A$

Violet light is, ${\delta_{\mathrm{v}}} }=\left(\mu_{\mathrm{cv}}+\mu_{\mathrm{fv}}-2\right) A$

Red light is, $\delta_{\mathrm{r}}=\left(\mu_{\mathrm{cr}}+\mu_{\mathrm{fr}}-2\right) A$

Step 3 :  

Angular dispersion combination :

$\delta_{v}-\delta_{r}=\left(\mu_{\mathrm{cv}}+\mu_{\mathrm{fv}}-2\right) A-\left(\mu_{\mathrm{cr}}+\mu_{\mathrm{fr}}-2\right) A$

           $=\left(\mu_{\mathrm{CV}}+\mu_{\mathrm{fv}}-\mu_{\mathrm{cr}}-\mu_{\mathrm{fr}}\right) A$

           $=(1.525+1.632-1.515-1.612) 5$

           = 0.15°

So, the combination produces angular dispersion of 0.15 °.

Answer 2

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The angular produced by the angle is of 0.15°