Question

In a direct vision spectroscope, there are two flint glass prisms, each of angle $6^{\circ }$, and three crown glass prisms. The dispersive powers of flint and crown glasses are $0.37$ and $0.23$ respectively and their refractive indices for mean color are $1.632$ and $1.554$ respectively. The net dispersion produced by the system of prisms is:

• A. $3^{\circ }{12}^{\prime }$
• B. $2^{\circ }{4}^{\prime }$
• C. $1^{\circ }{4}^{\prime }$
• D. ${1.5}^{\circ }{2}^{\prime }$

Answer 1

Answer: (C)

$1^{\circ }{4}^{\prime }$

We have two flint glass prisms.

If there is no deviation then we have,

$2\times ({\mu }_{y,1}-1)\times A_1+3\times ({\mu }_{y,2}-1)\times A_2=0$
$2(1.632-1)6^o+3(1.554-1)A^{\prime }=0$
$⟹A^{\prime }=-{4.56}^o$
The net dispersion can be written as
$2({\mu }_{v,1}-{\mu }_{r,1})A+3({\mu }_{v,2}-{\mu }_{r,2})A^{\prime }$
$=2{\omega }_1({\mu }_{y,1}-1)A+3{\omega }_2({\mu }_{y,2}-1)A^{\prime }$

$=[2\times 0.37\times (1.632-1)\times 6]+[3\times 0.23\times (1.554-1)\times (-4.56\left)\right]$

$=1^o{4}^{\prime }$