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  • An achromatic combination of two prisms - one of quartz and other of flint glass is to be formed. If the refracting angle of the quartz prism is <img alt="4^{\circ}" src="https://entrancecorner.onc

An achromatic combination of two prisms - one of quartz and other of flint glass is to be formed. If the refracting angle of the quartz prism is 4^{\circ}, find the refracting angle of the flint glass prism. Also find the net mean deviation produced by the combination. Given that for the flint glass : \mu_{\mathrm{v}}=1.694, \mu_{\mathrm{r}}=1.65 and for the quartz glass :\mu_{\mathrm{v}}=1.557, \mu_{\mathrm{r}}=1.542.

Option: 1

-1.282


Option: 2

+1.282


Option: 3

-5.282


Option: 4

-8.282


Answers (1)

For an achromatic combination, net dispersion =0
\Rightarrow dispersion by one prism = dispersion by other prism.

\mathrm{\Rightarrow\left(\mu_{1 v}-\mu_{1 r}\right) A_{1}=\left(\mu_{2 v}-\mu_{2 r}\right) A_{2} }
\mathrm{\Rightarrow(1.694-1.65) A_{1}=(1.557-1.542) \times 4 }
\mathrm{\Rightarrow A_{1}=1.364^{\circ} }

\mathrm{D_{m 1}-D_{m 2}=\left(\mu_{1 m}-1\right) A_{1}-\left(\mu_{2 m}-1\right) A_{2} }
\mathrm{=\left(\frac{\mu_{1 v}+\mu_{1 r}}{2}-1\right) \times 1.364-\left(\frac{1.557+1.542}{2}-1\right) \times 4}
\mathrm{=\quad-1.641^{\circ}, 2=-1.282}

\mathrm{\text { Net mean deviation }=\left|D_{m 1}-D_{m 2}\right|=-1.282}

Posted by

Ramraj Saini

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