Question

Two glass prisms $P_1$ and $P_2$ are to be combined together to produce dispersion without deviation. The angles of the prisms $P_1$ and $P_2$ are selected as $4^o$ and $3^o$ respectively. If the refractive index of prism $P_1$ is 1.54, then that of $P_2$ will be

• A. 1.48
• B. 1.58
• C. 1.62
• D. 1.72

Answer 1

Answer: (D)

1.72

Prism angle of first prism $A_1=4^o$

Its refractive index ${\mu }_1=1.54$

Prism angle of second prism prism $A_2=3^o$

Let refractive index of second prism be ${\mu }_2$.

For dispersion without deviation, net deviation of the ray must be zero i.e. ${\delta }_1-{\delta }_2=0$

$\therefore$ $({\mu }_1-1)A_1-({\mu }_2-1)A_2=0$

OR $(1.54-1)\left(4\right)-({\mu }_2-1)3=0$

OR ${\mu }_2-1=0.72$ $⟹{\mu }_2=1.72$