Question

A crown glass prism of refracting angle $8^0$ is combined with a flint glass prism to obtain deviation without dispersion. If the refractive indices for red and violet rays for the crown glass are 1.514 and 1.524 and for the flint glass are 1.645 and 1.665 respectively, the net deviation is

• A. ${1.53}^0$
• B. ${1.23}^0$
• C. ${1.44}^0$
• D. ${1.14}^0$

Answer 1

The correct option is B ${1.23}^0$

Angle of crown glass prism $\left(A\right)=8^{\circ }$

For crown

${\mu }_{\gamma }=1.514{\mu }_V=1.524,\mu =\frac{1.514+1.524}{2}=1.5195$

For flint glass

${\mu }^{\prime }\gamma =1.645{\mu }^{\prime }v=1.665,{\mu }^{\prime }=\frac{1.645+1.665}{2}=1.650$

Condition for no dispersion is.

-) deviation in crown = devition in flint glass

$\begin{array}{cc}& dv-d\gamma =d^{\prime }v-d\gamma \\ \Rightarrow & ({\mu }_V-{\mu }_{\gamma })A=({\mu }_v^{\prime }-{\mu }_{\gamma }^{\prime }\gamma )A^{\prime }\\ & A^{\prime }=\text{angle in flint glass}\end{array}$

$\begin{array}{cc}(1.52.5-1.514)8& =(1.665-1.645)A^{\prime }\\ 0.011\times 8& =0.020\times n^{\prime }\\ \therefore A^{\prime }& =\frac{0,011\times 8}{0,020}\\ \therefore A^{\prime }& ={4.4}^0\end{array}$

$\begin{array}{cc}\text{Mean deviation}& =d-d^{\prime }\\ & =(\mu -1)A-({\mu }^{\prime }-1)R^{\prime }\\ & =[\mu ,{\mu }^{\prime }\text{are avg values}\}\\ & =(1.5195-1)8-(1.650-1)4.4\\ & =0.5195\times 8-0.650\times 4.4\\ & =4.156-2.86\\ & \Rightarrow 1.296\\ & \approx 1.23\left(\text{nearest}\right)\end{array}$

$\text{Hence}\left(B\right)\text{is correct option.}$