Question

Find the angle of the flint glass prism, which should be combined with a crown glass prism of $5^{\circ }$ to give dispersion but no deviation.
For crown glass: ${\mu }_v=1.523;{\mu }_R=1.515$
For flint glass : ${\mu }^{\prime }{}_v=1.688;{\mu }^{\prime }{}_R=1.650$

• A. $5^{\circ }$
• B. ${3.87}^{\circ }$
• C. ${1.65}^{\circ }$
• D. ${2.5}^{\circ }$

Answer 1

The correct option is B ${3.87}^{\circ }$

For no deviation:

$A^{\prime }=\left(\frac{\mu -1}{{\mu }^{\prime }-1}\right)A$

Here,

$\mu =\frac{{\mu }_v+{\mu }_R}{2}=\frac{1.523+1.515}{2}=1.519$

${\mu }^{\prime }=\frac{{\mu }_v^{\prime }+{\mu }_R^{\prime }}{2}=\frac{1.668+1.650}{2}=1.669$

$\therefore A^{\prime }=\left(\frac{1.519-1}{1.669-1}\right)5^{\circ }={3.87}^{\circ }$

Hence, $\left(\text{B}\right)$ is the correct answer.