Question

Dispersion without deviation is produced by two thin (small angled) prisms which are combined. One prism has angle $6^{\circ }$ and refractive index $1.52$. If the other prism has an angle $4^{\circ }$, what is its refractive index ?

• A. $1.64$
• B. $1.17$
• C. $1.78$
• D. $1.48$

Answer 1

The correct option is C $1.78$

If the angles of the two prisms are $A_1$ and $A_2$ and refractive indices are ${\mu }_1$ and ${\mu }_2$

Given that,
${\mu }_1=1.52;A_1=6^{\circ };A_2=4^{\circ };$

Using formula for dispersion without deviation

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

$\Rightarrow (1.52-1)6=({\mu }_2-1)4$

$\Rightarrow ({\mu }_2-1)=\frac{6}{4}\times 0.52=0.78$

$\Rightarrow {\mu }_2=0.78+1=1.78$

Hence, option $\left(d\right)$ is correct.